Optimal decay rates for the compressible Navier–Stokes equations with density–dependent viscosities

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-06-05 DOI:10.1016/j.jde.2025.113483

Zhen Luo, Wanying Yang

引用次数: 0

Abstract

This paper concerns the Cauchy problem for the compressible Navier–Stokes equations with density-dependent viscosities, and the optimal decay rates of all higher order spatial derivatives of the solutions are obtained. We also prove the same optimal decay rates of solution to the shallow water equations with capillarity. The proof relies on applying the high-low frequency decomposition in the pure energy estimates developed by Guo and Wang (2012) [11], both linearly and nonlinearly.

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具有密度依赖粘度的可压缩Navier-Stokes方程的最优衰减率

本文研究了具有密度依赖黏度的可压缩Navier-Stokes方程的Cauchy问题，得到了其解的所有高阶空间导数的最优衰减率。我们还证明了具有毛细作用的浅水方程解的最优衰减率。该证明依赖于在郭和王（2012）[11]开发的纯能量估计中应用高低频分解，包括线性和非线性。

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

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics