Small data global regularity and scattering for 3D Ericksen–Leslie compressible hyperbolic liquid crystal model

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2019-05-13 DOI:10.1142/S0219891622500199

Jiaxi Huang, Ning Jiang, Yi-Long Luo, Lifeng Zhao

引用次数: 5

Abstract

We study the Ericksen–Leslie hyperbolic system for compressible liquid crystal model in three spatial dimensions. Global regularity and scattering for small and smooth initial data near equilibrium are proved for the case that the system is a nonlinear coupling of compressible Navier–Stokes equations with wave map to [Formula: see text]. The main strategy relies on an interplay between the control of high order energies and decay estimates, which is based on the idea inspired by the method of space-time resonances. Unlike the incompressible model, the different behaviors of the decay properties of the density and velocity field for compressible fluids at different frequencies play a key role, which is a particular feature of compressible model.

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三维Ericksen–Leslie可压缩双曲型液晶模型的小数据全局正则性和散射

我们研究了三维可压缩液晶模型的Ericksen–Leslie双曲系统。对于系统是具有波动图的可压缩Navier-Stokes方程的非线性耦合的情况，证明了接近平衡的小而光滑初始数据的全局正则性和散射性。主要策略依赖于高阶能量控制和衰变估计之间的相互作用，这是基于时空共振方法启发的思想。与不可压缩模型不同，可压缩流体在不同频率下密度场和速度场衰减特性的不同行为起着关键作用，这是可压缩模型的一个特殊特征。

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

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.