Endpoint regularity criterion for weak solutions of the 3D incompressible liquid crystals system

被引：2

作者：

Men, Yueyang ^{[1
]}

Wang, Wendong ^{[2
,3
]}

Wu, Gang ^{[4
]}

机构：

[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[3] Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 10期

基金：

中国国家自然科学基金;

关键词：

backward uniqueness; liquid crystals system; regularity criterion; NAVIER-STOKES EQUATIONS; WELL-POSEDNESS; FLOW; UNIQUENESS;

D O I：

10.1002/mma.4854

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the endpoint case regularity for the 3D liquid crystals system. We prove that if vL(0,T;L3(R3)), then weak solution (v,d) is smooth, and our main observation is that the condition delta dL(0,T;L3(R3)) is not necessary in this situation. The proof is based on the blow-up analysis and backward uniqueness for the parabolic operator developed by Escauriaza-Seregin-Sverak.

引用

页码：3672 / 3683

页数：12

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