Global well-posedness to the Cauchy problem of 2D compressible nematic liquid crystal flows with large initial data and vacuum

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-01-13 DOI:10.1007/s00208-023-02794-5

Xin Zhong, Xuan Zhou

引用次数: 0

Abstract

We study compressible nematic liquid crystal flows with the bulk viscosity being a power function of the density (\(\lambda =\rho ^\beta \)) on the whole two-dimensional (2D) plane. Under a geometric angle condition for the initial direction field, we show the global existence and uniqueness of strong solutions provided that \(\beta >\frac{4}{3}\). It should be noticed that there is no other restrictions on the size of initial data and the initial density allows vacuum states.

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具有大初始数据和真空的二维可压缩向列液晶流的 Cauchy 问题的全局好拟性

我们研究了在整个二维（2D）平面上体积粘度是密度（\lambda =\rho ^\beta \）的幂函数的可压缩向列液晶流。在初始方向场的几何角度条件下，我们证明了强（\(\beta >\frac{4}{3}\ ）解的全局存在性和唯一性。需要注意的是，初始数据的大小没有其他限制，初始密度允许真空状态。

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

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.