Pub Date : 2026-01-14DOI: 10.1016/j.na.2026.114057
Mostafa Meliani
We study the local existence of solutions to the Navier–Stokes–Fourier-magnetohydrodynamics (NSF-MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the Lp–Lq class with inhomogeneous boundary conditions. The open system is allowed to receive incoming matter from the outside through (part of) the boundary which we refer to as an inflow boundary. This setup brings about a difficulty in estimating the regularity of the density ϱ which we remedy by assuming appropriate hypotheses on the velocity field, domain boundary and on the boundary and initial data of ϱ. The main result ensures the local well-posedness of the full NSF-MHD system which is shown through a linearization combined with a Banach fixed-point theorem.
{"title":"Lp–Lq existence for the open compressible MHD system","authors":"Mostafa Meliani","doi":"10.1016/j.na.2026.114057","DOIUrl":"10.1016/j.na.2026.114057","url":null,"abstract":"<div><div>We study the local existence of solutions to the Navier–Stokes–Fourier-magnetohydrodynamics (NSF-MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the <em>L<sup>p</sup></em>–<em>L<sup>q</sup></em> class with inhomogeneous boundary conditions. The open system is allowed to receive incoming matter from the outside through (part of) the boundary which we refer to as an inflow boundary. This setup brings about a difficulty in estimating the regularity of the density ϱ which we remedy by assuming appropriate hypotheses on the velocity field, domain boundary and on the boundary and initial data of ϱ. The main result ensures the local well-posedness of the full NSF-MHD system which is shown through a linearization combined with a Banach fixed-point theorem.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"267 ","pages":"Article 114057"},"PeriodicalIF":1.3,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979449","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 : 2026-01-05DOI: 10.1016/j.na.2025.114054
Daniel Goodair
We obtain energy estimates for a transport and stretching noise under Leray Projection on a 2D bounded convex domain, in Sobolev Spaces of arbitrarily high order. The estimates are taken in equivalent inner products, defined through powers of the Stokes Operator with a specific choice of Navier boundary conditions. We exploit fine properties of the noise in relation to the Stokes Operator to achieve cancellation of derivatives in the presence of the Leray Projector. As a result, we achieve an additional degree of regularity in the corresponding Stochastic Navier-Stokes Equation to attain a true strong solution of the original Stratonovich equation. Furthermore for any order of smoothness, we can construct a strong solution of a hyperdissipative version of the Stochastic Navier-Stokes Equation with the given regularity; hyperdissipation is only required to control the nonlinear term in the presence of a boundary. We supplement the result by obtaining smoothness without hyperdissipation on the torus, in 2D and 3D on the lifetime of solutions.
{"title":"High order smoothness for stochastic Navier-Stokes equations with transport and stretching noise on bounded domains","authors":"Daniel Goodair","doi":"10.1016/j.na.2025.114054","DOIUrl":"10.1016/j.na.2025.114054","url":null,"abstract":"<div><div>We obtain energy estimates for a transport and stretching noise under Leray Projection on a 2D bounded convex domain, in Sobolev Spaces of arbitrarily high order. The estimates are taken in equivalent inner products, defined through powers of the Stokes Operator with a specific choice of Navier boundary conditions. We exploit fine properties of the noise in relation to the Stokes Operator to achieve cancellation of derivatives in the presence of the Leray Projector. As a result, we achieve an additional degree of regularity in the corresponding Stochastic Navier-Stokes Equation to attain a true strong solution of the original Stratonovich equation. Furthermore for any order of smoothness, we can construct a strong solution of a hyperdissipative version of the Stochastic Navier-Stokes Equation with the given regularity; hyperdissipation is only required to control the nonlinear term in the presence of a boundary. We supplement the result by obtaining smoothness without hyperdissipation on the torus, in 2D and 3D on the lifetime of solutions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"267 ","pages":"Article 114054"},"PeriodicalIF":1.3,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928323","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 : 2026-01-03DOI: 10.1016/j.na.2025.114046
Sergio Zamora , Xingyu Zhu
For a polycyclic group Λ, rank(Λ) is defined as the number of factors in a polycyclic decomposition of Λ. For a finitely generated group G, rank(G) is defined as the infimum of rank(Λ) among finite index polycyclic subgroups Λ ≤ G.
For a compact RCD(K, N) space with diam(X) ≤ ε(K, N), the rank of π1(X) is at most N. We show that in case of equality, X is homeomorphic to an infranilmanifold, generalizing a result by Kapovitch–Wilking to the non-smooth setting.
{"title":"Topological rigidity of small RCD(K,N) spaces with maximal rank","authors":"Sergio Zamora , Xingyu Zhu","doi":"10.1016/j.na.2025.114046","DOIUrl":"10.1016/j.na.2025.114046","url":null,"abstract":"<div><div>For a polycyclic group Λ, rank(Λ) is defined as the number of <span><math><mi>Z</mi></math></span> factors in a polycyclic decomposition of Λ. For a finitely generated group <em>G</em>, rank(<em>G</em>) is defined as the infimum of rank(Λ) among finite index polycyclic subgroups Λ ≤ <em>G</em>.</div><div>For a compact RCD(<em>K, N</em>) space <span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></math></span> with diam(<em>X</em>) ≤ ε(<em>K, N</em>), the rank of <em>π</em><sub>1</sub>(<em>X</em>) is at most <em>N</em>. We show that in case of equality, <em>X</em> is homeomorphic to an infranilmanifold, generalizing a result by Kapovitch–Wilking to the non-smooth setting.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"267 ","pages":"Article 114046"},"PeriodicalIF":1.3,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886071","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 : 2025-12-31DOI: 10.1016/j.na.2025.114030
Dieter Bothe, Pierre-Étienne Druet, Robert Haller
We consider elliptic transmission problems in several space dimensions near an interface which is C1,1-diffeomorphic to an axisymmetric reference interface with a singular point of cusp type. We establish the regularity of the gradient and of the Hessian in Lp spaces up to the cusp point for local weak solutions. We obtain regularity thresholds which are different according to whether the cusp is inward or outward to the subdomain, and which depend explicitly on the opening of the interface at the cusp. Our results allow for source terms in the bulk and on the interface.
{"title":"Gradient and Hessian regularity in elliptic transmission problems near a point cusp","authors":"Dieter Bothe, Pierre-Étienne Druet, Robert Haller","doi":"10.1016/j.na.2025.114030","DOIUrl":"10.1016/j.na.2025.114030","url":null,"abstract":"<div><div>We consider elliptic transmission problems in several space dimensions near an interface which is <em>C</em><sup>1,1</sup>-diffeomorphic to an axisymmetric reference interface with a singular point of cusp type. We establish the regularity of the gradient and of the Hessian in <em>L<sup>p</sup></em> spaces up to the cusp point for local weak solutions. We obtain regularity thresholds which are different according to whether the cusp is inward or outward to the subdomain, and which depend explicitly on the opening of the interface at the cusp. Our results allow for source terms in the bulk and on the interface.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114030"},"PeriodicalIF":1.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884533","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 : 2025-12-26DOI: 10.1016/j.na.2025.114044
Enrique Aguilar , Bashar Khorbatly
We consider the system of partial differential equations proposed in [1] as an alternative to the Navier-Stokes equations. These two sets of equations differ primarily in that the former incorporates diffusive terms of mass, momentum and energy. While existence of solutions to a weak version of the diffusive system is demonstrated in [1], we further reduce the diffusive differential equations and their weak counterparts using the isentropic assumption. Under specific technical assumptions, we establish a form of uniqueness known as weak-strong uniqueness for the reduced systems. This ensures that a solution to the differential equations and a solution to the weak counterpart are equivalent provided they originate from the same initial data.
{"title":"Weak-strong uniqueness in an alternative system to the isentropic Navier-Stokes equations","authors":"Enrique Aguilar , Bashar Khorbatly","doi":"10.1016/j.na.2025.114044","DOIUrl":"10.1016/j.na.2025.114044","url":null,"abstract":"<div><div>We consider the system of partial differential equations proposed in [1] as an alternative to the Navier-Stokes equations. These two sets of equations differ primarily in that the former incorporates diffusive terms of mass, momentum and energy. While existence of solutions to a weak version of the diffusive system is demonstrated in <span><span>[1]</span></span>, we further reduce the diffusive differential equations and their weak counterparts using the isentropic assumption. Under specific technical assumptions, we establish a form of uniqueness known as weak-strong uniqueness for the reduced systems. This ensures that a solution to the differential equations and a solution to the weak counterpart are equivalent provided they originate from the same initial data.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114044"},"PeriodicalIF":1.3,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840534","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 : 2025-12-26DOI: 10.1016/j.na.2025.114045
Chen-Gang Long , Senping Luo , Wenming Zou
In this paper, we consider the minimization problem of two dimensional lattice energyWe study this minimization problem under the classical Yukawa potential with α > 0, t > 1 and . We prove the existence of a critical value such that:
•
if then the minimizer corresponds to a hexagonal lattice configuration;
•
if then no minimizer exists.
This result provide the sharp bound βc for hexagonal lattice crystallization under Yukawa potential. Furthermore, we extend the analysis to two-component lattices, where each component is centered on the other, and obtain the same critical value βc. In this case, the minimizer transitions between a rhombic-square-rectangular configuration and a scenario where no minimizer exists.
{"title":"On minima of lattice energy under Yukawa potentials","authors":"Chen-Gang Long , Senping Luo , Wenming Zou","doi":"10.1016/j.na.2025.114045","DOIUrl":"10.1016/j.na.2025.114045","url":null,"abstract":"<div><div>In this paper, we consider the minimization problem of two dimensional lattice energy<span><span><span><math><mrow><munder><mi>min</mi><mrow><mo>|</mo><mstyle><mi>Λ</mi></mstyle><mo>|</mo><mo>=</mo><mn>1</mn></mrow></munder><msub><mi>E</mi><mi>f</mi></msub><mrow><mo>(</mo><mstyle><mi>Λ</mi></mstyle><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mtext>where</mtext><mspace></mspace><msub><mi>E</mi><mi>f</mi></msub><mrow><mo>(</mo><mstyle><mi>Λ</mi></mstyle><mo>)</mo></mrow><mo>=</mo><munder><mo>∑</mo><mrow><mi>P</mi><mo>∈</mo><mstyle><mi>Λ</mi></mstyle><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></mrow></munder><msup><mrow><mi>f</mi><mo>(</mo><mo>|</mo><mi>P</mi><mo>|</mo></mrow><mn>2</mn></msup><mrow><mo>)</mo><mo>.</mo></mrow></mrow></math></span></span></span>We study this minimization problem under the classical Yukawa potential <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo>=</mo><mfrac><msup><mi>e</mi><mrow><mo>−</mo><mi>α</mi><mi>π</mi><mi>r</mi></mrow></msup><mi>r</mi></mfrac><mo>−</mo><mi>β</mi><mfrac><msup><mi>e</mi><mrow><mo>−</mo><mi>t</mi><mi>α</mi><mi>π</mi><mi>r</mi></mrow></msup><mi>r</mi></mfrac></mrow></math></span> with <em>α</em> > 0, <em>t</em> > 1 and <span><math><mrow><mi>β</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. We prove the existence of a critical value <span><math><mrow><msub><mi>β</mi><mi>c</mi></msub><mo>=</mo><mn>1</mn></mrow></math></span> such that:<ul><li><span>•</span><span><div>if <span><math><mrow><mi>β</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mi>∞</mi><mo>,</mo><msub><mi>β</mi><mi>c</mi></msub><mo>]</mo><mo>,</mo></mrow></math></span> then the minimizer corresponds to a hexagonal lattice configuration;</div></span></li><li><span>•</span><span><div>if <span><math><mrow><mi>β</mi><mo>∈</mo><mo>(</mo><msub><mi>β</mi><mi>c</mi></msub><mo>,</mo><mo>+</mo><mi>∞</mi><mo>)</mo><mo>,</mo></mrow></math></span> then no minimizer exists.</div></span></li></ul></div><div>This result provide the sharp bound <em>β<sub>c</sub></em> for hexagonal lattice crystallization under Yukawa potential. Furthermore, we extend the analysis to two-component lattices, where each component is centered on the other, and obtain the same critical value <em>β<sub>c</sub></em>. In this case, the minimizer transitions between a rhombic-square-rectangular configuration and a scenario where no minimizer exists.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114045"},"PeriodicalIF":1.3,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840535","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 : 2025-12-23DOI: 10.1016/j.na.2025.114043
Matteo Caggio , Gabriele Sbaiz
We consider the Navier-Stokes-Fourier system for a heat conducting compressible fluid under the effects of rotation and stratification. We investigate the low Mach, Rossby and Froude number limit towards a quasi-geostrophic balance in a stratification range between the so-called low and strong stratification regimes. The limit is studied in the context of weak solutions with ill-prepared initial data.
{"title":"Between low and strong stratification regimes for rotating heat-conducting fluids","authors":"Matteo Caggio , Gabriele Sbaiz","doi":"10.1016/j.na.2025.114043","DOIUrl":"10.1016/j.na.2025.114043","url":null,"abstract":"<div><div>We consider the Navier-Stokes-Fourier system for a heat conducting compressible fluid under the effects of rotation and stratification. We investigate the low Mach, Rossby and Froude number limit towards a quasi-geostrophic balance in a stratification range between the so-called low and strong stratification regimes. The limit is studied in the context of weak solutions with ill-prepared initial data.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114043"},"PeriodicalIF":1.3,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840533","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 : 2025-12-22DOI: 10.1016/j.na.2025.114037
Mirella Aoun
In this paper, we consider the following class of nonlinear parabolic equations with non-homogeneous Neumann boundary conditions:where Ω is a bounded open domain of , N ≥ 2 and T > 0. Assuming that f, resp. h belong to L1(QT), resp. L1(0, T; L1(∂Ω)), while g is an element of L2(QT)N and u is a vector field verifying specific conditions, we prove the existence and uniqueness of renormalized solutions.
{"title":"Existence and uniqueness of renormalized solutions for parabolic Neumann problem with L1 data","authors":"Mirella Aoun","doi":"10.1016/j.na.2025.114037","DOIUrl":"10.1016/j.na.2025.114037","url":null,"abstract":"<div><div>In this paper, we consider the following class of nonlinear parabolic equations with non-homogeneous Neumann boundary conditions:<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mrow><mfrac><mrow><mi>∂</mi><mi>θ</mi></mrow><mrow><mi>∂</mi><mi>t</mi></mrow></mfrac><mo>−</mo><mi>div</mi><mrow><mo>(</mo><mi>A</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>θ</mi><mo>)</mo><mi>∇</mi><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mi>θ</mi><mo>=</mo><mi>f</mi><mo>−</mo><mi>div</mi><mi>g</mi></mrow></mtd><mtd><mrow><mtext>in</mtext><mspace></mspace><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>θ</mi><mrow><mo>(</mo><mi>t</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mi>θ</mi><mn>0</mn></msub></mrow></mtd><mtd><mrow><mtext>in</mtext><mspace></mspace><mstyle><mi>Ω</mi></mstyle><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mo>(</mo><mi>A</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>θ</mi><mo>)</mo></mrow><mi>∇</mi><mi>θ</mi><mo>−</mo><mi>g</mi><mo>)</mo><mo>·</mo><mover><mi>n</mi><mo>→</mo></mover><mo>=</mo><mi>h</mi></mrow></mtd><mtd><mrow><mtext>on</mtext><mspace></mspace><mi>∂</mi><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo><mo>,</mo></mrow></mtd></mtr></mtable></mrow></math></span></span></span>where Ω is a bounded open domain of <span><math><msup><mi>R</mi><mi>N</mi></msup></math></span>, <em>N</em> ≥ 2 and <em>T</em> > 0. Assuming that <em>f</em>, resp. <em>h</em> belong to <em>L</em><sup>1</sup>(<em>Q<sub>T</sub></em>), resp. <em>L</em><sup>1</sup>(0, <em>T</em>; <em>L</em><sup>1</sup>(∂Ω)), while <em>g</em> is an element of <em>L</em><sup>2</sup>(<em>Q<sub>T</sub></em>)<sup><em>N</em></sup> and <em>u</em> is a vector field verifying specific conditions, we prove the existence and uniqueness of renormalized solutions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114037"},"PeriodicalIF":1.3,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840532","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 : 2025-12-19DOI: 10.1016/j.na.2025.114039
Taiki Takeuchi
We consider the Keller–Segel system of parabolic-elliptic type with logistic growth in the whole space , where n ≥ 3, 1 < κ < 2, and l ∈ {0, 1}. We show the existence and uniqueness of local mild solutions u for initial data under the conditions n/2 < p < n, 1 ≤ q ≤ ∞, and 2p/n < κ < 2. In addition, partial smoothing effects of the mild solutions u are investigated. More precisely, we show that u satisfy the original system in a classical sense and have the property . According to the regularities of the term with the power nonlinearity, such regularities for u seem to be optimal under the general framework beyond the physical sense.
我们考虑在整个空间Rn上具有logistic增长u - |u|κ - lul的抛物-椭圆型Keller-Segel系统，其中n ≥ 3,1 <； κ <； 2，且l ∈ {0,1}。我们展示当地温和解的存在性和唯一性u初始数据∈Bp,问−2 + n / p (Rn)条件下n / 2 & lt; p & lt; n, 1 ≤ 问 ≤ ∞,和2 p / n & lt; κ & lt; 2。此外，还研究了温和溶液u的部分平滑效应。更准确地说，我们证明了u满足经典意义上的原始系统，并且具有u∈clockk +1((0,T];L∞(Rn))∩Lloc∞(（0,T];Cκ+2(Rn)）的性质。从|u|κ−l项的幂非线性规律来看，在超出物理意义的一般框架下，u的这种规律似乎是最优的。
{"title":"Partial smoothing effects of local mild solutions of the Keller–Segel system with logistic growth in Besov spaces","authors":"Taiki Takeuchi","doi":"10.1016/j.na.2025.114039","DOIUrl":"10.1016/j.na.2025.114039","url":null,"abstract":"<div><div>We consider the Keller–Segel system of parabolic-elliptic type with logistic growth <span><math><mrow><mi>u</mi><mo>−</mo><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>κ</mi><mo>−</mo><mi>l</mi></mrow></msup><msup><mi>u</mi><mi>l</mi></msup></mrow></math></span> in the whole space <span><math><msup><mi>R</mi><mi>n</mi></msup></math></span>, where <em>n</em> ≥ 3, 1 < <em>κ</em> < 2, and <em>l</em> ∈ {0, 1}. We show the existence and uniqueness of local mild solutions <em>u</em> for initial data <span><math><mrow><mi>a</mi><mo>∈</mo><msubsup><mi>B</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mo>−</mo><mn>2</mn><mo>+</mo><mi>n</mi><mo>/</mo><mi>p</mi></mrow></msubsup><mrow><mo>(</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> under the conditions <em>n</em>/2 < <em>p</em> < <em>n</em>, 1 ≤ <em>q</em> ≤ ∞, and 2<em>p</em>/<em>n</em> < <em>κ</em> < 2. In addition, partial smoothing effects of the mild solutions <em>u</em> are investigated. More precisely, we show that <em>u</em> satisfy the original system in a classical sense and have the property <span><math><mrow><mi>u</mi><mo>∈</mo><msubsup><mi>C</mi><mrow><mtext>loc</mtext></mrow><mrow><mi>κ</mi><mo>+</mo><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>;</mo><msup><mi>L</mi><mi>∞</mi></msup><mrow><mo>(</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow><mo>)</mo></mrow><mo>∩</mo><msubsup><mi>L</mi><mrow><mtext>loc</mtext></mrow><mi>∞</mi></msubsup><mrow><mo>(</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>;</mo><msup><mi>C</mi><mrow><mi>κ</mi><mo>+</mo><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>. According to the regularities of the term <span><math><mrow><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>κ</mi><mo>−</mo><mi>l</mi></mrow></msup><msup><mi>u</mi><mi>l</mi></msup></mrow></math></span> with the power nonlinearity, such regularities for <em>u</em> seem to be optimal under the general framework beyond the physical sense.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114039"},"PeriodicalIF":1.3,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797903","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 : 2025-12-19DOI: 10.1016/j.na.2025.114042
Flank D.M. Bezerra , Vando Narciso , Senlin Yan
This paper is dedicated to the analysis of the pullback dynamics of a non-autonomous Balakrishnan-Taylor beam with a strong damping dependent on the time and linear energy of the system. In the main result we establish the existence of a pullback attractor for the evolution process generated by the weak solutions of the system. In addition, we also prove a result of upper semicontiunity of attractors with respect to functional parameters present in the damped term.
{"title":"Pullback dynamics for a class of plate equations with time-dependent energy damping","authors":"Flank D.M. Bezerra , Vando Narciso , Senlin Yan","doi":"10.1016/j.na.2025.114042","DOIUrl":"10.1016/j.na.2025.114042","url":null,"abstract":"<div><div>This paper is dedicated to the analysis of the pullback dynamics of a non-autonomous Balakrishnan-Taylor beam with a strong damping dependent on the time and linear energy of the system. In the main result we establish the existence of a pullback attractor for the evolution process generated by the weak solutions of the system. In addition, we also prove a result of upper semicontiunity of attractors with respect to functional parameters present in the damped term.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114042"},"PeriodicalIF":1.3,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797902","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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