On the Global Regularity of the Two-Dimensional Density Patch for Inhomogeneous Incompressible Viscous Flow

被引：19

作者：

Liao, Xian ^{[1
]}

Zhang, Ping ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2016年 / 220卷 / 03期

关键词：

NAVIER-STOKES EQUATIONS; VORTEX PATCHES; VARIABLE-DENSITY; BOUNDED DENSITY; FLUID; EXISTENCE; CALCULUS; VELOCITY; POCKETS; SPACE;

D O I：

10.1007/s00205-015-0945-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Regarding P.-L. Lions' open question in Oxford Lecture Series in Mathematics and its Applications, Vol. 3 (1996) concerning the propagation of regularity for the density patch, we establish the global existence of solutions to the two-dimensional inhomogeneous incompressible Navier-Stokes system with initial density given by for some small enough constant and some domain , with initial vorticity belonging to and with appropriate tangential regularities. Furthermore, we prove that the regularity of the domain is preserved by time evolution.

引用

页码：937 / 981

页数：45

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