Spatial Decay/Asymptotics in the Navier–Stokes Equation

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI:10.1134/S1061920824601812

P. Topalov

引用次数: 0

Abstract

We discuss the occurrence of spatial asymptotic expansions of solutions to the Navier–Stokes equation on \( {\mathbb{R}} ^d\). In particular, we prove that the Navier–Stokes equation is locally well-posed in a class of weighted Sobolev and asymptotic spaces. The solutions depend analytically on the initial data and time and (generically) develop nontrivial asymptotic terms as \(|x|\to\infty\). In addition, the solutions have a spatial smoothing property that depends on the order of the asymptotic expansion.

DOI 10.1134/S1061920824601812

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Navier-Stokes方程的空间衰减/渐近性

讨论了在\( {\mathbb{R}} ^d\)上Navier-Stokes方程解的空间渐近展开式的出现。特别地，我们证明了Navier-Stokes方程在一类加权Sobolev和渐近空间中是局部适定的。解解析地依赖于初始数据和时间，并且（一般地）发展为非平凡渐近项，如\(|x|\to\infty\)。此外，解具有空间平滑性质，该性质依赖于渐近展开的阶数。Doi 10.1134/ s1061920824601812

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.