Global Existence of Weak Solutions for a Model of Nematic Liquid Crystal-Colloidal Interactions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI:10.1137/23m161149x

Zhiyuan Geng, Arnab Roy, Arghir Zarnescu

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4324-4355, August 2024.
Abstract. In this paper, we study a mathematical model describing the movement of a colloidal particle in a fixed, bounded three dimensional container filled with a nematic liquid crystal fluid. The motion of the fluid is governed by the Beris–Edwards model for nematohydrodynamics equations, which couples the incompressible Navier–Stokes equations with a parabolic system. The dynamics of colloidal particle within the nematic liquid crystal is described by the conservation laws of linear and angular momentum. We prove the existence of global weak solutions for the coupled system.

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向列液晶-胶体相互作用模型弱解的全局存在性

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4324-4355 页，2024 年 8 月。摘要本文研究了一个描述胶体粒子在充满向列液晶流体的固定有界三维容器中运动的数学模型。流体的运动受向立流体力学方程的 Beris-Edwards 模型控制，该模型将不可压缩的纳维-斯托克斯方程与抛物线系统耦合在一起。向列液晶中胶体粒子的动力学由线性和角动量守恒定律描述。我们证明了耦合系统存在全局弱解。

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

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.