REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW  

作　　者：Daomin CAO Shuangjie PENG Shusen YAN 曹道珉;彭双阶;严树森(Institute of Applied Mathematics, Chinese Academy of Science;School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences,Central China Normal University;Department of Mathematics, The University of New England Armidale)

机构地区：[1]Institute of Applied Mathematics,Chinese Academy of Science,Beijing 100190,China [2]School of Mathematics and Statistics ＆ Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,Chin [3]Department of Mathematics,The University of New England Armidale,NSW 2351,Australia

出　　处：《Acta Mathematica Scientia》2018年第5期1443-1467,共25页数学物理学报（B辑英文版）

摘　　要：In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations{-△u=λ∑1Bδ（x0,j）（u-kj）p＋,in Ω,u=0,onΩ is a bounded simply-connected smooth domain, ki （i = 1,… , k） is prescribed positive constant. The result we prove is that for any given non-degenerate critical pointX0=（x0,1,…,x0,k of the Kirchhoff-Routh function defined on Ωk corresponding to （ k1,……kk ）there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→＋∞ shrinks to {x05}, and the local vorticity strength near each x0,j approaches kj, j = 1,… , k. This result makes the study of the above problem with p _〉 0 complete since the cases p 〉 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations{-△u=λ∑1Bδ（x0,j）（u-kj）p＋,in Ω,u=0,onΩ is a bounded simply-connected smooth domain, ki （i = 1,… , k） is prescribed positive constant. The result we prove is that for any given non-degenerate critical pointX0=（x0,1,…,x0,k of the Kirchhoff-Routh function defined on Ωk corresponding to （ k1,……kk ）there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→＋∞ shrinks to {x05}, and the local vorticity strength near each x0,j approaches kj, j = 1,… , k. This result makes the study of the above problem with p _〉 0 complete since the cases p 〉 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.

关 键 词：REGULARIZATION planar vortices vorticity sets REDUCTION 

分 类 号：O175.25[理学—数学]