Archive for Rational Mechanics and Analysis最新文献_第4页

Carleman Factorization of Layer Potentials on Smooth Domains 光滑域上层势的Carleman分解

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-14 DOI: 10.1007/s00205-025-02106-y

Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi, Mihai Putinar

引用次数: 0

Global Smooth Solutions to the Landau–Coulomb Equation in (L^{3/2}) 中Landau-Coulomb方程的全局光滑解 (L^{3/2})

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-12 DOI: 10.1007/s00205-025-02107-x

William Golding, Maria Gualdani, Amélie Loher

{"title":"Global Smooth Solutions to the Landau–Coulomb Equation in (L^{3/2})","authors":"William Golding, Maria Gualdani, Amélie Loher","doi":"10.1007/s00205-025-02107-x","DOIUrl":"10.1007/s00205-025-02107-x","url":null,"abstract":"<div>We consider the homogeneous Landau equation in ({mathbb {R}}^3) with Coulomb potential and initial data in polynomially weighted (L^{3/2}). We show that there exists a smooth solution that is bounded for all positive times. The proof is based on short-time regularization estimates for the Fisher information, which, combined with the recent result of Guillen and Silvestre, yields the existence of a global-in-time smooth solution. Additionally, if the initial data belongs to (L^p) with (p>3/2), there is a unique solution. At the crux of the result is a new (varepsilon )-regularity criterion in the spirit of the Caffarelli–Kohn–Nirenberg theorem: a solution which is small in weighted (L^{3/2}) is regular. Although the (L^{3/2}) norm is a critical quantity for the Landau–Coulomb equation, using this norm to measure the regularity of solutions presents significant complications. For instance, the (L^{3/2}) norm alone is not enough to control the (L^infty ) norm of the competing reaction and diffusion coefficients. These analytical challenges caused prior methods relying on the parabolic structure of the Landau–Coulomb to break down. Our new framework is general enough to handle slowly decaying and singular initial data, and provides the first proof of global well-posedness for the Landau–Coulomb equation with rough initial data.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02107-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Non-unique Ergodicity for Deterministic and Stochastic 3D Navier–Stokes and Euler Equations 确定性和随机三维Navier-Stokes和Euler方程的非唯一遍历性

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-10 DOI: 10.1007/s00205-025-02102-2

Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu

{"title":"Non-unique Ergodicity for Deterministic and Stochastic 3D Navier–Stokes and Euler Equations","authors":"Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu","doi":"10.1007/s00205-025-02102-2","DOIUrl":"10.1007/s00205-025-02102-2","url":null,"abstract":"<div>We establish the existence of infinitely many statistically stationary solutions, as well as ergodic statistically stationary solutions, to the three dimensional Navier–Stokes and Euler equations in both deterministic and stochastic settings, driven by additive noise. These solutions belong to the regularity class (C({{mathbb {R}}};H^{vartheta })cap C^{vartheta }({{mathbb {R}}};L^{2})) for some (vartheta >0) and satisfy the equations in an analytically weak sense. The solutions to the Euler equations are obtained as vanishing viscosity limits of statistically stationary solutions to the Navier–Stokes equations. Furthermore, regardless of their construction, every statistically stationary solution to the Euler equations within this regularity class, which satisfies a suitable moment bound, is a limit in law of statistically stationary analytically weak solutions to Navier–Stokes equations with vanishing viscosities. Our results are based on a novel stochastic version of the convex integration method, which provides uniform moment bounds in the aforementioned function spaces.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143932324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Optimal Rate of Vortex Stretching for Axisymmetric Euler Flows Without Swirl 无旋流轴对称欧拉流的最优涡旋拉伸速率

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-09 DOI: 10.1007/s00205-025-02103-1

Deokwoo Lim, In-Jee Jeong

引用次数: 0

Long-Time Behavior of an Arc-Shaped Vortex Filament and Its Application to the Stability of a Circular Vortex Filament 弧形涡丝的长时间特性及其在圆涡丝稳定性中的应用

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-08 DOI: 10.1007/s00205-025-02104-0

Masashi Aiki

{"title":"Long-Time Behavior of an Arc-Shaped Vortex Filament and Its Application to the Stability of a Circular Vortex Filament","authors":"Masashi Aiki","doi":"10.1007/s00205-025-02104-0","DOIUrl":"10.1007/s00205-025-02104-0","url":null,"abstract":"<div>We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We show stability estimates for an arc-shaped vortex filament, which is an exact solution to an initial-boundary value problem for the Localized Induction Equation. An arc-shaped filament travels along an axis at a constant speed without changing its shape, and is oriented in such a way that the arc stays in a plane that is perpendicular to the axis. We prove that an arc-shaped filament is stable in the Lyapunov sense for general perturbations except in the axis-direction, for which the perturbation can grow linearly in time. We also show that this estimate is optimal. We then apply the obtained stability estimates to study the stability of a circular vortex filament under some symmetry assumptions on the initial perturbation. We do this by dividing the circular filament into arcs, apply the stability estimate to each arc-shaped filament, and combine the estimates to obtain estimates for the whole circle. The optimality of the stability estimates for an arc-shaped filament also shows that a circular filament is not stable in the Lyapunov sense, namely, certain perturbations can grow linearly in time.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02104-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Weakly Coupled Two-Dimensional Fermi Polaron 弱耦合二维费米极化子

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-05 DOI: 10.1007/s00205-025-02098-9

David Mitrouskas

引用次数: 0

Limiting Behavior of Minimizing p-Harmonic Maps in 3d as p Goes to 2 with Finite Fundamental Group 有限基本群p→2时三维p调和映射最小化的极限行为

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-04-24 DOI: 10.1007/s00205-025-02086-z

Bohdan Bulanyi, Jean Van Schaftingen, Benoît Van Vaerenbergh

{"title":"Limiting Behavior of Minimizing p-Harmonic Maps in 3d as p Goes to 2 with Finite Fundamental Group","authors":"Bohdan Bulanyi, Jean Van Schaftingen, Benoît Van Vaerenbergh","doi":"10.1007/s00205-025-02086-z","DOIUrl":"10.1007/s00205-025-02086-z","url":null,"abstract":"<div>We study the limiting behavior of minimizing p-harmonic maps from a bounded Lipschitz domain (Omega subset mathbb {R}^{3}) to a compact connected Riemannian manifold without boundary and with finite fundamental group as (p nearrow 2). We prove that there exists a closed set (S_{*}) of finite length such that minimizing p-harmonic maps converge to a locally minimizing harmonic map in (Omega setminus S_{*}). We prove that locally inside (Omega ) the singular set (S_{*}) is a finite union of straight line segments, and it minimizes the mass in the appropriate class of admissible chains. Furthermore, we establish local and global estimates for the limiting singular harmonic map. Under additional assumptions, we prove that globally in (overline{Omega }) the set (S_{*}) is a finite union of straight line segments, and it minimizes the mass in the appropriate class of admissible chains, which is defined by a given boundary datum and (Omega ).\u0000</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02086-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hölder Regularity of the Pressure for Weak Solutions of the 3D Euler Equations in Bounded Domains Hölder有界区域内三维欧拉方程弱解压力的规律性

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-04-17 DOI: 10.1007/s00205-025-02090-3

Claude Bardos, Daniel W. Boutros, Edriss S. Titi

{"title":"Hölder Regularity of the Pressure for Weak Solutions of the 3D Euler Equations in Bounded Domains","authors":"Claude Bardos, Daniel W. Boutros, Edriss S. Titi","doi":"10.1007/s00205-025-02090-3","DOIUrl":"10.1007/s00205-025-02090-3","url":null,"abstract":"<div>We consider the three-dimensional incompressible Euler equations on a bounded domain (Omega ) with (C^4) boundary. We prove that if the velocity field (u in C^{0,alpha } (Omega )) with (alpha > 0) (where we are omitting the time dependence), it follows that the corresponding pressure p of a weak solution to the Euler equations belongs to the Hölder space (C^{0, alpha } (Omega )). We also prove that away from the boundary p has (C^{0,2alpha }) regularity. In order to prove these results we use a local parametrisation of the boundary and a very weak formulation of the boundary condition for the pressure of the weak solution, as was introduced in Bardos and Titi (Philos Trans R Soc A 380, 20210073, 2022), which is different than the commonly used boundary condition for classical solutions of the Euler equations. Moreover, we provide an explicit example illustrating the necessity of this new very weak formulation of the boundary condition for the pressure. Furthermore, we also provide a rigorous derivation of this new formulation of the boundary condition for weak solutions of the Euler equations. This result is of importance for the proof of the first half of the Onsager Conjecture, the sufficient conditions for energy conservation of weak solutions to the three-dimensional incompressible Euler equations in bounded domains. In particular, the results in this paper remove the need for separate regularity assumptions on the pressure in the proof of the Onsager conjecture.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143845664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The inviscid inflow-outflow problem via analyticity 用解析法求解无粘流入流出问题

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-04-14 DOI: 10.1007/s00205-025-02095-y

Igor Kukavica, Wojciech Ożański, Marco Sammartino

引用次数: 0

Time-Harmonic Maxwell’s Equations in Periodic Waveguides 周期波导中的时谐麦克斯韦方程组

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-04-10 DOI: 10.1007/s00205-025-02099-8

A. Kirsch, B. Schweizer

引用次数: 0