非平稳Navier-Stokes方程弱解压力函数的正则性

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2023-11-23 DOI:10.1134/s0012266123090069

E. V. Amosova

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引用次数: 0

摘要

研究不可压缩流体的非定常Navier-Stokes方程组。基于一个考虑速度场弛豫为螺线场的正则化问题，证明了在Hopf类解的考虑域中几乎处处存在压力函数。利用提出的正则化方法，我们证明了原问题存在更正则的弱解，而不受原始数据的小约束。在二维情况下证明了唯一性定理。

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Regularity of the Pressure Function for Weak Solutions of the Nonstationary Navier–Stokes Equations

Abstract

We study the nonstationary system of Navier–Stokes equations for an incompressible fluid. Based on a regularized problem that takes into account the relaxation of the velocity field into a solenoidal field, the existence of a pressure function almost everywhere in the domain under consideration for solutions in the Hopf class is substantiated. Using the proposed regularization, we prove the existence of more regular weak solutions of the original problem without smallness restrictions on the original data. A uniqueness theorem is proven in the two-dimensional case.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.