Pub Date : 2026-01-01Epub Date: 2025-11-13DOI: 10.1016/j.physd.2025.135035
Lianjie Song, Wei Liang, Qiu Du
A tri-neuron discrete-time BAM neural network with two delays is considered in this paper. When the network satisfies several relatively weak conditions, one criterion of stability is established. Moreover, proof of the existence of chaos in the sense of Li–Yorke and Devaney is given by applying the snap-back repeller theory. One example is demonstrated by showing its chaotic behavior and the trends of the largest Lyapunov exponent, which further illustrates the correctness of the obtained results.
{"title":"Dynamics analysis of a tri-neuron discrete-time BAM neural network with two delays","authors":"Lianjie Song, Wei Liang, Qiu Du","doi":"10.1016/j.physd.2025.135035","DOIUrl":"10.1016/j.physd.2025.135035","url":null,"abstract":"<div><div>A tri-neuron discrete-time BAM neural network with two delays is considered in this paper. When the network satisfies several relatively weak conditions, one criterion of stability is established. Moreover, proof of the existence of chaos in the sense of Li–Yorke and Devaney is given by applying the snap-back repeller theory. One example is demonstrated by showing its chaotic behavior and the trends of the largest Lyapunov exponent, which further illustrates the correctness of the obtained results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135035"},"PeriodicalIF":2.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-10-28DOI: 10.1016/j.physd.2025.135002
Wenjing Xing , Nan Liu , Jinyi Sun
In this study, we present a systematical inverse scattering transform for the matrix modified Korteweg–de Vries (mKdV) equation with the associated analytic scattering coefficients consisting of pairs of higher-order zeros. The analyticity properties and symmetries of the Jost eigenfunctions and scattering coefficients are discussed in the direct problem. In particular, discrete spectrum associated with these pairs of multiple zeros is analyzed explicitly. Next, we formulate a 4 × 4 matrix Riemann–Hilbert (RH) problem that incorporates the residue conditions at these higher-order poles. By solving this RH problem, we obtain the reconstruction formula for the solution of the matrix mKdV equation. Under the reflectionless condition, the associated RH problem can be reduced to a system of linear algebraic equations. We demonstrate that the solution to this system exists and is unique, allowing us to explicitly derive the higher-order soliton solutions.
{"title":"On the inverse scattering transform for the matrix mKdV equation with multiple higher-order poles","authors":"Wenjing Xing , Nan Liu , Jinyi Sun","doi":"10.1016/j.physd.2025.135002","DOIUrl":"10.1016/j.physd.2025.135002","url":null,"abstract":"<div><div>In this study, we present a systematical inverse scattering transform for the matrix modified Korteweg–de Vries (mKdV) equation with the associated analytic scattering coefficients consisting of <span><math><mi>N</mi></math></span> pairs of higher-order zeros. The analyticity properties and symmetries of the Jost eigenfunctions and scattering coefficients are discussed in the direct problem. In particular, discrete spectrum associated with these <span><math><mi>N</mi></math></span> pairs of multiple zeros is analyzed explicitly. Next, we formulate a 4 × 4 matrix Riemann–Hilbert (RH) problem that incorporates the residue conditions at these higher-order poles. By solving this RH problem, we obtain the reconstruction formula for the solution of the matrix mKdV equation. Under the reflectionless condition, the associated RH problem can be reduced to a system of linear algebraic equations. We demonstrate that the solution to this system exists and is unique, allowing us to explicitly derive the higher-order soliton solutions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 135002"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-10-03DOI: 10.1016/j.physd.2025.134963
Francisco J. Herranz , Danilo Latini
This work aims to bridge the gap between Dunkl superintegrable systems and the coalgebra symmetry approach to superintegrability, and subsequently to recover known models and construct new ones. In particular, an infinite family of -dimensional quasi-maximally superintegrable quantum systems with reflections, sharing the same set of quantum integrals, is introduced. The result is achieved by introducing a novel differential–difference realization of and then applying the coalgebra formalism. Several well-known maximally superintegrable models with reflections appear as particular cases of this general family, among them, the celebrated Dunkl oscillator and the Dunkl–Kepler–Coulomb system. Furthermore, restricting to the case of “hidden” quantum quadratic symmetries, maximally superintegrable curved oscillator and Kepler–Coulomb Hamiltonians of Dunkl type, sharing the same underlying coalgebra symmetry, are presented. Namely, the Dunkl oscillator and the Dunkl–Kepler–Coulomb system on the -sphere and hyperbolic space together with two models which can be interpreted as a one-parameter superintegrable deformation of the Dunkl oscillator and the Dunkl–Kepler–Coulomb system on non-constant curvature spaces. In addition, maximally superintegrable generalizations of these models, involving non-central potentials, are also derived on flat and curved spaces. For all specific systems, at least an additional quantum integral is explicitly provided, which is related to the Dunkl version of a (curved) Demkov–Fradkin tensor or a Laplace–Runge–Lenz vector.
{"title":"An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler–Coulomb models","authors":"Francisco J. Herranz , Danilo Latini","doi":"10.1016/j.physd.2025.134963","DOIUrl":"10.1016/j.physd.2025.134963","url":null,"abstract":"<div><div>This work aims to bridge the gap between Dunkl superintegrable systems and the coalgebra symmetry approach to superintegrability, and subsequently to recover known models and construct new ones. In particular, an infinite family of <span><math><mi>N</mi></math></span>-dimensional quasi-maximally superintegrable quantum systems with reflections, sharing the same set of <span><math><mrow><mn>2</mn><mi>N</mi><mo>−</mo><mn>3</mn></mrow></math></span> quantum integrals, is introduced. The result is achieved by introducing a novel differential–difference realization of <span><math><mrow><mi>sl</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> and then applying the coalgebra formalism. Several well-known maximally superintegrable models with reflections appear as particular cases of this general family, among them, the celebrated Dunkl oscillator and the Dunkl–Kepler–Coulomb system. Furthermore, restricting to the case of “hidden” quantum quadratic symmetries, maximally superintegrable curved oscillator and Kepler–Coulomb Hamiltonians of Dunkl type, sharing the same underlying <span><math><mrow><mi>sl</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> coalgebra symmetry, are presented. Namely, the Dunkl oscillator and the Dunkl–Kepler–Coulomb system on the <span><math><mi>N</mi></math></span>-sphere and hyperbolic space together with two models which can be interpreted as a one-parameter superintegrable deformation of the Dunkl oscillator and the Dunkl–Kepler–Coulomb system on non-constant curvature spaces. In addition, maximally superintegrable generalizations of these models, involving non-central potentials, are also derived on flat and curved spaces. For all specific systems, at least an additional quantum integral is explicitly provided, which is related to the Dunkl version of a (curved) Demkov–Fradkin tensor or a Laplace–Runge–Lenz vector.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134963"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-09-02DOI: 10.1016/j.physd.2025.134923
Benno Rumpf , Alan C. Newell
Wave turbulence of weakly nonlinear dispersive waves is a disordered state in which energy or other conserved quantities are transferred from sources in wavenumber space (the driving range) to sinks (the dissipation range). The theory of wave turbulence provides an analytic derivation of all statistical quantities (most notably the Kolmogorov–Zakharov spectrum) from the underlying equations of motion. A competing and radically different turbulent process with a significant impact on the statistical properties is the formation of coherent structures. Under what conditions can we observe purely weak wave turbulence, and when is it superseded by coherent structures? We study this problem for an influential model of one-dimensional turbulent dynamics, the Majda–McLaughlin–Tabak equation. The formation of narrow radiating solitary waves (pulses) leads to spectra that are steeper than the Kolmogorov–Zakharov spectra. However, for sufficiently large box sizes, we find that wave turbulence prevails within a broad range of four orders of magnitude of the driving force.
{"title":"The competition between wave turbulence and coherent structures","authors":"Benno Rumpf , Alan C. Newell","doi":"10.1016/j.physd.2025.134923","DOIUrl":"10.1016/j.physd.2025.134923","url":null,"abstract":"<div><div>Wave turbulence of weakly nonlinear dispersive waves is a disordered state in which energy or other conserved quantities are transferred from sources in wavenumber space (the driving range) to sinks (the dissipation range). The theory of wave turbulence provides an analytic derivation of all statistical quantities (most notably the Kolmogorov–Zakharov spectrum) from the underlying equations of motion. A competing and radically different turbulent process with a significant impact on the statistical properties is the formation of coherent structures. Under what conditions can we observe purely weak wave turbulence, and when is it superseded by coherent structures? We study this problem for an influential model of one-dimensional turbulent dynamics, the Majda–McLaughlin–Tabak equation. The formation of narrow radiating solitary waves (pulses) leads to spectra that are steeper than the Kolmogorov–Zakharov spectra. However, for sufficiently large box sizes, we find that wave turbulence prevails within a broad range of four orders of magnitude of the driving force.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134923"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-09-08DOI: 10.1016/j.physd.2025.134924
Manohar Teja Kalluri, Andrew Hillier
The non-linear regime of the magnetic Rayleigh–Taylor instability (MRTI) has been studied in the context of several laboratory and astrophysical systems. Yet, several fundamental aspects remain unclear. One of them is the self-similar evolution of the instability. Studies have assumed that non-linear MRTI has a self-similar, quadratic growth similar to hydrodynamic (HD) RTI. However, neither self-similarity nor quadratic growth has been proved analytically. Furthermore, an explicit understanding of the factors that control the growth of non-linear instability remains unclear. Magnetic fields are known to play a crucial role in the evolution of the instability. Yet, a systematic study discussing how the magnetic field influences the instability growth is missing. These issues were addressed by performing an analytical and numerical study of the MRTI with a uniform magnetic field. Our study reveals that the imposed magnetic field does not conform to the HD self-similar evolution. However, the influence of the imposed magnetic field decays with time () as relative to the other non-linear terms, making the MRTI conform to the HD self-similarity. Thus, the HD RTI self-similar scaling becomes relevant to MRTI at late times, when nonlinear dynamics dominate. Based on energy conservation, an equation for the mixing layer height () is derived, which demonstrates the quadratic growth of in time. This gave insight into various factors that could influence the non-linear growth of the instability. By studying MRTI at different magnetic field strengths, we demonstrate the role of magnetic field strength on the nonlinear growth of MRTI. Thus, the current study analytically and numerically proves the role of magnetic fields on the evolution of MRTI.
{"title":"Self-similarity and growth of non-linear magnetic Rayleigh–Taylor instability — Role of the magnetic field strength","authors":"Manohar Teja Kalluri, Andrew Hillier","doi":"10.1016/j.physd.2025.134924","DOIUrl":"10.1016/j.physd.2025.134924","url":null,"abstract":"<div><div>The non-linear regime of the magnetic Rayleigh–Taylor instability (MRTI) has been studied in the context of several laboratory and astrophysical systems. Yet, several fundamental aspects remain unclear. One of them is the self-similar evolution of the instability. Studies have assumed that non-linear MRTI has a self-similar, quadratic growth similar to hydrodynamic (HD) RTI. However, neither self-similarity nor quadratic growth has been proved analytically. Furthermore, an explicit understanding of the factors that control the growth of non-linear instability remains unclear. Magnetic fields are known to play a crucial role in the evolution of the instability. Yet, a systematic study discussing how the magnetic field influences the instability growth is missing. These issues were addressed by performing an analytical and numerical study of the MRTI with a uniform magnetic field. Our study reveals that the imposed magnetic field does not conform to the HD self-similar evolution. However, the influence of the imposed magnetic field decays with time (<span><math><mi>t</mi></math></span>) as <span><math><mrow><mn>1</mn><mo>/</mo><mi>t</mi></mrow></math></span> relative to the other non-linear terms, making the MRTI conform to the HD self-similarity. Thus, the HD RTI self-similar scaling becomes relevant to MRTI at late times, when nonlinear dynamics dominate. Based on energy conservation, an equation for the mixing layer height (<span><math><mi>h</mi></math></span>) is derived, which demonstrates the quadratic growth of <span><math><mi>h</mi></math></span> in time. This gave insight into various factors that could influence the non-linear growth of the instability. By studying MRTI at different magnetic field strengths, we demonstrate the role of magnetic field strength on the nonlinear growth of MRTI. Thus, the current study analytically and numerically proves the role of magnetic fields on the evolution of MRTI.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134924"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145047382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-11-10DOI: 10.1016/j.physd.2025.135030
Márcio Cavalcante , Ailton C. Nascimento
We study special regularity properties of solutions to the initial–boundary value problem associated with the Korteweg–de Vries equations posed on the positive half-line. In particular, for initial data and boundary data , where the restriction of to some subset of has an extra regularity for any , we prove that the regularity of solutions moves with infinite speed to its left as time evolves until a certain time . The existence of a stopping time appears because of the effect of the boundary function . Also, as a consequence of our proof, we prove a gain in the regularity of the trace derivatives of the solutions for the Korteweg–de Vries on the half-line.
{"title":"On the propagation of regularity of solutions to the KdV equation on the positive half-line","authors":"Márcio Cavalcante , Ailton C. Nascimento","doi":"10.1016/j.physd.2025.135030","DOIUrl":"10.1016/j.physd.2025.135030","url":null,"abstract":"<div><div>We study special regularity properties of solutions to the initial–boundary value problem associated with the Korteweg–de Vries equations posed on the positive half-line. In particular, for initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span> and boundary data <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where the restriction of <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> to some subset of <span><math><mrow><mo>(</mo><mi>b</mi><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span> has an extra regularity for any <span><math><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow></math></span>, we prove that the regularity of solutions <span><math><mi>u</mi></math></span> moves with infinite speed to its left as time evolves until a certain time <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. The existence of a stopping time <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> appears because of the effect of the boundary function <span><math><mi>f</mi></math></span>. Also, as a consequence of our proof, we prove a gain in the regularity of the trace derivatives of the solutions for the Korteweg–de Vries on the half-line.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135030"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-09-08DOI: 10.1016/j.physd.2025.134925
Sergey Dyachenko , Dmitry E. Pelinovsky
We address Euler’s equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profiles. In agreement with the previous numerical results, we give a rigorous proof that the zero eigenvalue bifurcation in the linearized equations of motion for co-periodic perturbations occurs at each extremal point of the energy function versus the steepness parameter, provided that the wave speed is not extremal at the same steepness. We derive the leading order of the unstable eigenvalues and, assisted with numerical approximation of its coefficients, we show that the new unstable eigenvalues emerge only in the direction of increasing steepness.
{"title":"Bifurcations of unstable eigenvalues for Stokes waves derived from conserved energy","authors":"Sergey Dyachenko , Dmitry E. Pelinovsky","doi":"10.1016/j.physd.2025.134925","DOIUrl":"10.1016/j.physd.2025.134925","url":null,"abstract":"<div><div>We address Euler’s equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profiles. In agreement with the previous numerical results, we give a rigorous proof that the zero eigenvalue bifurcation in the linearized equations of motion for co-periodic perturbations occurs at each extremal point of the energy function versus the steepness parameter, provided that the wave speed is not extremal at the same steepness. We derive the leading order of the unstable eigenvalues and, assisted with numerical approximation of its coefficients, we show that the new unstable eigenvalues emerge only in the direction of increasing steepness.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134925"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-10-11DOI: 10.1016/j.physd.2025.134974
N.V. Stankevich
We study the structure of bifurcation lines of the equilibrium state and limit cycles depending on the parameters in a three-dimensional oscillator demonstrating autonomous quasi-periodic oscillations. It is shown that soft and hard birth of a stable invariant torus is possible. The birth of a torus in a hard way can occur from a stable equilibrium state. We localize the regions of coexistence of multistable hidden self-oscillatory attractors with a stable equilibrium state in the parameter space. We describe in details mechanisms of birth/destroying of multistable hidden attractors associated with the co-dimension 2 bifurcations and the crises.
{"title":"Soft and hard appearance of torus and codimension two bifurcations in three-dimensional autonomous quasi-periodic oscillator","authors":"N.V. Stankevich","doi":"10.1016/j.physd.2025.134974","DOIUrl":"10.1016/j.physd.2025.134974","url":null,"abstract":"<div><div>We study the structure of bifurcation lines of the equilibrium state and limit cycles depending on the parameters in a three-dimensional oscillator demonstrating autonomous quasi-periodic oscillations. It is shown that soft and hard birth of a stable invariant torus is possible. The birth of a torus in a hard way can occur from a stable equilibrium state. We localize the regions of coexistence of multistable hidden self-oscillatory attractors with a stable equilibrium state in the parameter space. We describe in details mechanisms of birth/destroying of multistable hidden attractors associated with the co-dimension 2 bifurcations and the crises.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134974"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-10-14DOI: 10.1016/j.physd.2025.134967
D. Breit , A. Roy
We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier–Stokes equations in a domain that is evolving in accordance with the motion of the structure. The displacement of the latter evolves according to a beam equation. The two systems are coupled through kinematic boundary conditions and balance of forces. We prove that for any weak solution to the coupled system that additionally satisfies certain regularity conditions, contact between the elastic wall and the bottom of the fluid cavity cannot occur. This conditional no-contact result applies to both isentropic and heat-conducting fluids.
{"title":"Compressible fluids and elastic plates in 2D: A conditional no-contact theorem","authors":"D. Breit , A. Roy","doi":"10.1016/j.physd.2025.134967","DOIUrl":"10.1016/j.physd.2025.134967","url":null,"abstract":"<div><div>We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier–Stokes equations in a domain that is evolving in accordance with the motion of the structure. The displacement of the latter evolves according to a beam equation. The two systems are coupled through kinematic boundary conditions and balance of forces. We prove that for any weak solution to the coupled system that additionally satisfies certain regularity conditions, contact between the elastic wall and the bottom of the fluid cavity cannot occur. This conditional no-contact result applies to both isentropic and heat-conducting fluids.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134967"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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