Steady vortex patches near a nontrivial irrotational flow  

作　　者：Daomin Cao Guodong Wang Weicheng Zhan 

机构地区：[1]Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science China Mathematics》2021年第5期947-962,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11331010);supported by National Natural Science Foundation of China (Grant No.11771469);Chinese Academy of Sciences (Grant No.QYZDJ-SSW-SYS021)。

摘　　要：In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function q corresponding to a nontrivial irrotational flow, there exists a family of steady vortex patches approaching the set of extreme points of q on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of q corresponds to a family of steady multiple vortex patches approaching it.

关 键 词：Euler equation incompressible fluids vortex patch variational problem irrotational flow 

分 类 号：O357.1[理学—流体力学]