On global solutions to the inhomogeneous, incompressible Navier–Stokes equations with temperature-dependent coefficients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-01 DOI:10.4310/cms.2024.v22.n2.a6

Bijun Zuo

引用次数: 0

Abstract

In this paper, we study the initial-boundary value problem for the full inhomogeneous, incompressible Navier–Stokes equations with temperature-dependent viscosity and heat conductivity coefficients. The viscosity coefficient may be degenerate in the sense that it may vanish in the region of absolutely zero temperature. Our main result is to prove the global existence of large weak solutions to such a system. The proof is based on a three-level approximate scheme, the Galerkin method, De Giorgi’s method, and appropriate compactness arguments.

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关于具有温度相关系数的非均质不可压缩纳维-斯托克斯方程的全局解决方案

本文研究了具有与温度相关的粘性系数和导热系数的完全不均匀、不可压缩纳维-斯托克斯方程的初始边界值问题。粘度系数可能是退化的，即它可能在温度绝对为零的区域消失。我们的主要结果是证明这种系统的大弱解的全局存在性。证明基于三层近似方案、Galerkin 方法、De Giorgi 方法和适当的紧凑性论证。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.