Archive for Rational Mechanics and Analysis最新文献

Global Solutions of the One-Dimensional Compressible Euler Equations with Nonlocal Interactions via the Inviscid Limit 具有非局部相互作用的一维可压缩欧拉方程的无粘极限全局解

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-24 DOI: 10.1007/s00205-025-02097-w

José A. Carrillo, Gui-Qiang G. Chen, Difan Yuan, Ewelina Zatorska

引用次数: 0

The Discrete Dislocation Dynamics of Multiple Dislocation Loops 多位错环的离散位错动力学

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-20 DOI: 10.1007/s00205-025-02108-w

Stefania Patrizi, Mary Vaughan

引用次数: 0

Transverse Linear Stability of One-Dimensional Solitary Gravity Water Waves 一维孤立重力水波的横向线性稳定性

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2025-05-15 DOI: 10.1007/s00205-025-02101-3

Frédéric Rousset, Changzhen Sun

引用次数: 0

Carleman Factorization of Layer Potentials on Smooth Domains

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