Remarks on the Uniqueness of Weak Solutions of the Incompressible Navier–Stokes Equations

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

Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI:10.1134/S1061920824030154

K.N. Soltanov

引用次数: 0

Abstract

This paper studies the uniqueness of a weak solution of the incompressible Navier–Stokes Equations in the 3-dimensional case. Here the investigation is provided by using two different approaches. The first (the main) result is obtained for given functions possessing a certain smoothness, using a new approach. The other result works without additional conditions but is, in some sense, a “local” result, investigated by another approach. In addition, here the solvability and uniqueness of weak solutions to the auxiliary problems derived from the main problem are investigated.

DOI 10.1134/S1061920824030154

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关于不可压缩纳维-斯托克斯方程弱解唯一性的评论

本文研究三维不可压缩纳维-斯托克斯方程弱解的唯一性。本文采用两种不同的方法进行研究。第一个（主要）结果是利用一种新方法，针对具有一定平滑性的给定函数得出的。另一个结果不需要附加条件，但在某种意义上是一个 "局部 "结果，通过另一种方法进行研究。此外，本文还研究了由主问题导出的辅助问题的弱解的可解性和唯一性。 doi 10.1134/s1061920824030154

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.