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

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

E. V. Amosova

引用次数: 0

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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非平稳Navier-Stokes方程弱解压力函数的正则性

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。

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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