论带周期性边界条件的不可压缩三维纳维-斯托克斯方程解的正则性

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI:10.1134/S1061920824020092

Qun Lin

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引用次数: 0

摘要

摘要本文证明了具有空间周期边界条件的三维不可压缩纳维-斯托克斯方程的涡度属于\(L^{\infty}(0,T;L^2(\Omega))\)，进而得到了全局平滑解的存在。我们的方法是构建一组辅助系统来近似涡度方程的原始系统。

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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On the Regularity of the Solution for Incompressible 3D Navier–Stokes Equation with Periodic Boundary Conditions

In this paper, we prove that the vorticity belongs to \(L^{\infty}(0,T;L^2(\Omega))\) for 3D incompressible Navier–Stokes equation with space-periodic boundary conditions, then the existence of a global smooth solution is obtained. Our approach is to construct a set of auxiliary systems to approximate the original system of vorticity equation.

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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.