Existence and decay of global strong solutions to the nonhomogeneous incompressible liquid crystal system with vacuum and density-dependent viscosity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-07 DOI:10.4310/cms.2024.v22.n1.a11

Xia Ye, Mingxuan Zhu

引用次数: 0

Abstract

This paper is concerned with the initial value problem of the three-dimensional nonhomogeneous incompressible liquid crystal system with vacuum and density-dependent viscosity. We prove the existence of global strong solution on $\mathbb{R}^3 \times (0,\infty)$ under the initial norm ${\lVert u_0 \rVert}_{\dot{H}^\alpha} + {\lVert \nabla d_0 \rVert}_{\dot{H}^\alpha} (1/2 \lt \alpha \leq 1)$ being suitably small. In addition, the algebraic decay rate estimates of the global strong solution are obtained.

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具有真空和密度粘度的非均质不可压缩液晶系统的全局强解的存在性和衰减性

本文关注具有真空和密度粘度的三维非均相不可压缩液晶系统的初值问题。我们证明了在初始规范 ${\lVert u_0 \rVert}_{\dot{H}^\alpha} + {\lVert \nabla d_0 \rVert}_{\dot{H}^\alpha} (1/2 \lt \alpha \leq 1)$ 适当小的条件下，在 $\mathbb{R}^3 \times (0,\infty)$ 上存在全局强解。此外，还得到了全局强解的代数衰减率估计值。

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.