Uniqueness of global weak solutions to the frame hydrodynamics for biaxial nematic phases in $\mathbb{R}^2$

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.a7

Sirui Li, Chenchen Wang, Jie Xu

引用次数: 0

Abstract

We consider the hydrodynamics for biaxial nematic phases described by a field of orthonormal frame, which can be derived from a molecular-theory-based tensor model. We prove the uniqueness of global weak solutions to the Cauchy problem of the frame hydrodynamics in dimension two. The proof is mainly based on the suitable weaker energy estimates within the Littlewood–Paley analysis. We take full advantage of the estimates of nonlinear terms with rotational derivatives on $SO(3)$, together with cancellation relations and dissipative structures of the biaxial frame system.

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$\mathbb{R}^2$ 中双轴向列相的框架流体力学全局弱解的唯一性

我们考虑了由正交框架场描述的双轴向列相的流体力学，该正交框架场可从基于分子理论的张量模型中导出。我们证明了二维框架流体力学 Cauchy 问题全局弱解的唯一性。证明主要基于 Littlewood-Paley 分析中合适的弱能量估计。我们充分利用了$SO(3)$上带有旋转导数的非线性项的估计，以及双轴框架系统的抵消关系和耗散结构。

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.