Pub Date : 2024-07-18DOI: 10.1088/1361-6544/ad5f6f
Hung D Nguyen and Anand U Oza
We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.
{"title":"The invariant measure of a walking droplet in hydrodynamic pilot–wave theory","authors":"Hung D Nguyen and Anand U Oza","doi":"10.1088/1361-6544/ad5f6f","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5f6f","url":null,"abstract":"We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"9 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1088/1361-6544/ad6113
Yamin Xiao and Jie Jiang
An initial-Neumann boundary value problem for a Keller–Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension . In this work, we prove that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of at most, the classical solution is uniformly-in-time bounded when , thus preventing the infinite-time explosion detected in the source-free counter-part. The cornerstone of our proof lies in an improved comparison argument and a construction of an entropy inequality.
{"title":"Prevention of infinite-time blowup by slightly super-linear degradation in a Keller–Segel system with density-suppressed motility","authors":"Yamin Xiao and Jie Jiang","doi":"10.1088/1361-6544/ad6113","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6113","url":null,"abstract":"An initial-Neumann boundary value problem for a Keller–Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension . In this work, we prove that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of at most, the classical solution is uniformly-in-time bounded when , thus preventing the infinite-time explosion detected in the source-free counter-part. The cornerstone of our proof lies in an improved comparison argument and a construction of an entropy inequality.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1088/1361-6544/ad6112
Paul Carter, Arjen Doelman, Annalisa Iuorio and Frits Veerman
Reaction-diffusion models describing interactions between vegetation and water reveal the emergence of several types of patterns and travelling wave solutions corresponding to structures observed in real-life. Increasing their accuracy by also considering the ecological factor known as autotoxicity has lead to more involved models supporting the existence of complex dynamic patterns. In this work, we include an additional carrying capacity for the biomass in a Klausmeier-type vegetation-water-autotoxicity model, which induces the presence of two asymptotically small parameters: ɛ, representing the usual scale separation in vegetation-water models, and δ, directly linked to autotoxicity. We construct three separate types of homoclinic travelling pulse solutions based on two different scaling regimes involving ɛ and δ, with and without a so-called superslow plateau. The relative ordering of the small parameters significantly influences the phase space geometry underlying the construction of the pulse solutions. We complement the analysis by numerical continuation of the constructed pulse solutions, and demonstrate their existence (and stability) by direct numerical simulation of the full partial differential equation model.
{"title":"Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model","authors":"Paul Carter, Arjen Doelman, Annalisa Iuorio and Frits Veerman","doi":"10.1088/1361-6544/ad6112","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6112","url":null,"abstract":"Reaction-diffusion models describing interactions between vegetation and water reveal the emergence of several types of patterns and travelling wave solutions corresponding to structures observed in real-life. Increasing their accuracy by also considering the ecological factor known as autotoxicity has lead to more involved models supporting the existence of complex dynamic patterns. In this work, we include an additional carrying capacity for the biomass in a Klausmeier-type vegetation-water-autotoxicity model, which induces the presence of two asymptotically small parameters: ɛ, representing the usual scale separation in vegetation-water models, and δ, directly linked to autotoxicity. We construct three separate types of homoclinic travelling pulse solutions based on two different scaling regimes involving ɛ and δ, with and without a so-called superslow plateau. The relative ordering of the small parameters significantly influences the phase space geometry underlying the construction of the pulse solutions. We complement the analysis by numerical continuation of the constructed pulse solutions, and demonstrate their existence (and stability) by direct numerical simulation of the full partial differential equation model.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"56 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1088/1361-6544/ad6128
Dongho Chae and Jihoon Lee
This paper is concerned with the Liouville type theorems for the steady incompressible magnetohydrodynamics (MHD) equations. We establish that the solution to the steady MHD equations is identically zero under the integrability assumptions on (v, b). We show that, in particular, a combination of a strong integrability condition on the velocity of a fluid and a weak integrability condition on the magnetic field gives a sufficient condition on the Liouville type theorems. Furthermore, we show that the combination of the growth condition of the potential for the fluid velocity and the integrability condition for the magnetic field leads to the triviality of the solution.
本文关注稳定不可压缩磁流体动力学（MHD）方程的柳维尔类型定理。我们确定，在 (v, b) 的可整性假设条件下，稳定 MHD 方程的解是等效零。我们特别指出，流体速度的强可整性条件和磁场的弱可整性条件的组合给出了刘维尔类型定理的充分条件。此外，我们还证明，流体速度势的增长条件与磁场的可整性条件相结合，会导致解的三重性。
{"title":"On Liouville type results for the stationary MHD in R3","authors":"Dongho Chae and Jihoon Lee","doi":"10.1088/1361-6544/ad6128","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6128","url":null,"abstract":"This paper is concerned with the Liouville type theorems for the steady incompressible magnetohydrodynamics (MHD) equations. We establish that the solution to the steady MHD equations is identically zero under the integrability assumptions on (v, b). We show that, in particular, a combination of a strong integrability condition on the velocity of a fluid and a weak integrability condition on the magnetic field gives a sufficient condition on the Liouville type theorems. Furthermore, we show that the combination of the growth condition of the potential for the fluid velocity and the integrability condition for the magnetic field leads to the triviality of the solution.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"42 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-16DOI: 10.1088/1361-6544/ad6055
Hua Qiu, Qi Wang and Shufang Wang
We estimate the upper and lower Lq-spectra of measures generated by a class of graph-directed planar non-conformal iterated function systems. These systems are composed of contractions with lower triangular pointwise Jacobian. The estimation provides a criterion for the existence of the Lq-spectra in certain case. As an application, we derive the box-counting dimension of planar self-affine sets generated by lower triangular matrices, whose geometric construction satisfies a finite overlapping type condition.
{"title":"L q -spectra of graph-directed planar non-conformal measures","authors":"Hua Qiu, Qi Wang and Shufang Wang","doi":"10.1088/1361-6544/ad6055","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6055","url":null,"abstract":"We estimate the upper and lower Lq-spectra of measures generated by a class of graph-directed planar non-conformal iterated function systems. These systems are composed of contractions with lower triangular pointwise Jacobian. The estimation provides a criterion for the existence of the Lq-spectra in certain case. As an application, we derive the box-counting dimension of planar self-affine sets generated by lower triangular matrices, whose geometric construction satisfies a finite overlapping type condition.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"47 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-16DOI: 10.1088/1361-6544/ad6057
Matthew Novack
In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 Nonlinearity13 249–55) and Eyink (2003 Nonlinearity16 137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s , , laws. We apply these computations to improve a recent result of Hofmanova et al (2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruè et al (2023 Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giri et al (2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.
在本论文中，我们探讨了确定性环境中湍流理论某些精确结果的有效性。受 Duchon 和 Robert (2000 Nonlinearity13 249-55) 和 Eyink (2003 Nonlinearity16 137) 工作的启发，主要工具是不可压缩欧拉方程和纳维-斯托克斯方程弱解的一些能量平衡等式。因此，我们证明了欧拉方程和纳维-斯托克斯方程的某些弱解满足确定性版本的科尔莫戈罗夫Ⅳ定律。我们运用这些计算改进了霍夫曼诺娃等人（2023 arXiv:2304.14470）的最新结果，该结果表明，布鲁埃等人（2023 Commun. Pure Appl. Anal.）此外，我们还证明了吉里等人最近构建的全局耗散三维欧拉流（2023 arXiv:2305.18509）满足柯尔莫哥洛夫定律的局部版本。
{"title":"Scaling laws and exact results in turbulence *","authors":"Matthew Novack","doi":"10.1088/1361-6544/ad6057","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6057","url":null,"abstract":"In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 Nonlinearity13 249–55) and Eyink (2003 Nonlinearity16 137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s , , laws. We apply these computations to improve a recent result of Hofmanova et al (2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruè et al (2023 Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giri et al (2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"30 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-16DOI: 10.1088/1361-6544/ad6056
B Carvalho and E Rego
We discuss different regularities on stable/unstable holonomies of cw-hyperbolic homeomorphisms and prove that if a cw-hyperbolic homeomorphism has continuous joint stable/unstable holonomies, then it has a dense set of periodic points in its non-wandering set. For that, we prove that the hyperbolic cw-metric (introduced in Artigue et al (2024 J. Differ. Equ.378 512–38)) can be adapted to be self-similar (as in Artigue (2018 Ergodic Theory Dyn. Syst.38 2422–46)) and, in this case, continuous joint stable/unstable holonomies are pseudo-isometric. We also prove transitivity of cw-hyperbolic homeomorphisms assuming that the stable/unstable holonomies are isometric. In the case the ambient space is a surface, we prove that a cwF-hyperbolic homeomorphism has continuous joint stable/unstable holonomies when every bi-asymptotic sector is regular.
我们讨论了 cw-双曲同构的稳定/不稳定全局性的不同规律性，并证明如果 cw-双曲同构具有连续的联合稳定/不稳定全局性，那么它的非漫游集中就有一组密集的周期点。为此，我们证明双曲 cw-metric（Artigue 等（2024 J. Differ. Equ.378 512-38）中引入）可以调整为自相似（如 Artigue（2018 Ergodic Theory Dyn. Syst.38 2422-46）），并且在这种情况下，连续联合稳定/不稳定全局是伪等距的。我们还证明了假设稳定/不稳定全等式的 cw-双曲同构的反转性。在环境空间是曲面的情况下，我们证明了当每个双渐近扇形都是正则时，cwF-双曲同构具有连续的联合稳定/不稳定全同性。
{"title":"Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms","authors":"B Carvalho and E Rego","doi":"10.1088/1361-6544/ad6056","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6056","url":null,"abstract":"We discuss different regularities on stable/unstable holonomies of cw-hyperbolic homeomorphisms and prove that if a cw-hyperbolic homeomorphism has continuous joint stable/unstable holonomies, then it has a dense set of periodic points in its non-wandering set. For that, we prove that the hyperbolic cw-metric (introduced in Artigue et al (2024 J. Differ. Equ.378 512–38)) can be adapted to be self-similar (as in Artigue (2018 Ergodic Theory Dyn. Syst.38 2422–46)) and, in this case, continuous joint stable/unstable holonomies are pseudo-isometric. We also prove transitivity of cw-hyperbolic homeomorphisms assuming that the stable/unstable holonomies are isometric. In the case the ambient space is a surface, we prove that a cwF-hyperbolic homeomorphism has continuous joint stable/unstable holonomies when every bi-asymptotic sector is regular.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"39 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-14DOI: 10.1088/1361-6544/ad4dfd
Philip Arathoon
We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The eigenvalues of the locked inertia tensor descend to shape-space and endow it with the geometric structure of a three-web with the property that any normal relative equilibrium occurs as a critical point of the potential restricted to a leaf from the web. To demonstrate the utility of this web structure we show how the spherical three-body problem gives rise to a web of Cayley cubics on the three-sphere, and use this to fully classify the relative equilibria for the case of equal masses.
{"title":"Relative equilibria of mechanical systems with rotational symmetry","authors":"Philip Arathoon","doi":"10.1088/1361-6544/ad4dfd","DOIUrl":"https://doi.org/10.1088/1361-6544/ad4dfd","url":null,"abstract":"We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The eigenvalues of the locked inertia tensor descend to shape-space and endow it with the geometric structure of a three-web with the property that any normal relative equilibrium occurs as a critical point of the potential restricted to a leaf from the web. To demonstrate the utility of this web structure we show how the spherical three-body problem gives rise to a web of Cayley cubics on the three-sphere, and use this to fully classify the relative equilibria for the case of equal masses.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"38 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-10DOI: 10.1088/1361-6544/ad5e56
Edgardo Villar-Sepúlveda and Alan Champneys
A wave bifurcation is the counterpart to a Turing instability in reaction–diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. Such bifurcations require at least three components and give rise to patterns that are periodic in both space and time. Depending on boundary conditions, these patterns can comprise either rotating or standing waves. Restricting to systems in one spatial dimension, complete formulae are derived for the evaluation of the coefficients of the weakly nonlinear normal form of the bifurcation up to order five, including those that determine the criticality of both rotating and standing waves. The formulae apply to arbitrary n-component systems ( ) and their evaluation is implemented in software which is made available as supplementary material. The theory is illustrated on two different versions of three-component reaction–diffusion models of excitable media that were previously shown to feature super- and subcritical wave instabilities and on a five-component model of two-layer chemical reaction. In each case, two-parameter bifurcation diagrams are produced to illustrate the connection between complex dispersion relations and different types of Hopf, Turing, and wave bifurcations, including the existence of several codimension-two bifurcations.
波分岔与反应扩散系统中的图灵不稳定性相对应，但临界波数对应的是纯虚数对而不是零时间特征值。这种分岔至少需要三个分量，并产生在空间和时间上都具有周期性的模式。根据边界条件的不同，这些模式可以由旋转波或驻波组成。限于一个空间维度的系统，我们推导出了完整的公式，用于评估分岔的弱非线性法线形式系数，最高可达五阶，包括那些决定旋转波和驻波临界度的系数。这些公式适用于任意的 n 分量系统（ ），其评估由软件实现，该软件作为补充材料提供。该理论在两个不同版本的可激发介质三分量反应扩散模型和一个双层化学反应五分量模型上得到了说明，前者曾被证明具有超临界和亚临界波不稳定性。在每种情况下，都绘制了双参数分岔图，以说明复杂弥散关系与不同类型的霍普夫分岔、图灵分岔和波分岔之间的联系，包括几种同维度-2 分岔的存在。
{"title":"Amplitude equations for wave bifurcations in reaction–diffusion systems","authors":"Edgardo Villar-Sepúlveda and Alan Champneys","doi":"10.1088/1361-6544/ad5e56","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5e56","url":null,"abstract":"A wave bifurcation is the counterpart to a Turing instability in reaction–diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. Such bifurcations require at least three components and give rise to patterns that are periodic in both space and time. Depending on boundary conditions, these patterns can comprise either rotating or standing waves. Restricting to systems in one spatial dimension, complete formulae are derived for the evaluation of the coefficients of the weakly nonlinear normal form of the bifurcation up to order five, including those that determine the criticality of both rotating and standing waves. The formulae apply to arbitrary n-component systems ( ) and their evaluation is implemented in software which is made available as supplementary material. The theory is illustrated on two different versions of three-component reaction–diffusion models of excitable media that were previously shown to feature super- and subcritical wave instabilities and on a five-component model of two-layer chemical reaction. In each case, two-parameter bifurcation diagrams are produced to illustrate the connection between complex dispersion relations and different types of Hopf, Turing, and wave bifurcations, including the existence of several codimension-two bifurcations.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"36 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-10DOI: 10.1088/1361-6544/ad5e2f
Qingqing Liu and Qian Yan
In this paper, we are concerned with the outflow problem on a simplified viscous vasculogenesis model in the half-line . Firstly, we establish the global-in-time asymptotic stability of the rarefaction wave. Secondly, we obtain the unique existence and decay property of the boundary layer by using stable manifold theorem. Moreover, the asymptotic stability and convergence rates of solution towards boundary layer are obtained. The appearance of concentration makes the stationary problem more difficult than Navier–Stokes equations or Navier–Stokes–Poisson equations.
{"title":"Asymptotic stability of rarefaction wave and boundary layer for outflow problem on the viscous vasculogenesis model *","authors":"Qingqing Liu and Qian Yan","doi":"10.1088/1361-6544/ad5e2f","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5e2f","url":null,"abstract":"In this paper, we are concerned with the outflow problem on a simplified viscous vasculogenesis model in the half-line . Firstly, we establish the global-in-time asymptotic stability of the rarefaction wave. Secondly, we obtain the unique existence and decay property of the boundary layer by using stable manifold theorem. Moreover, the asymptotic stability and convergence rates of solution towards boundary layer are obtained. The appearance of concentration makes the stationary problem more difficult than Navier–Stokes equations or Navier–Stokes–Poisson equations.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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