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Steady vortex patch solutions to the vortex-wave system
Cao, Daomin1,2; Wang, Guodong2,3
Source PublicationNONLINEARITY
AbstractThe vortex-wave system describes the motion of a two-dimensional ideal fluid in which the vorticity includes continuously distributed vorticity, which is called the background vorticity, and a finite number of concentrated vortices. In this paper we restrict ourselves to the case of a single point vortex in a planar bounded domain. We prove that there exists a family of steady solutions to this system whose background vorticity is a vortex patch with prescribed distribution. Moreover, we show that these vortex patches 'shrink' to a minimum point of the Kirchhoff-Routh function as the strength parameter of the background vorticity goes to infinity.
Keywordvortex-wave system vortex patch Euler equation Kirchhoff-Routh function maximization desingularization
Funding ProjectNNSF of China[11771469] ; Chinese Academy of Sciences[QYZDJ-SSW-SYS021]
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000464717200002
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Document Type期刊论文
Corresponding AuthorCao, Daomin
Affiliation1.Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510405, Guangdong, Peoples R China
2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Cao, Daomin,Wang, Guodong. Steady vortex patch solutions to the vortex-wave system[J]. NONLINEARITY,2019,32(5):1882-1904.
APA Cao, Daomin,&Wang, Guodong.(2019).Steady vortex patch solutions to the vortex-wave system.NONLINEARITY,32(5),1882-1904.
MLA Cao, Daomin,et al."Steady vortex patch solutions to the vortex-wave system".NONLINEARITY 32.5(2019):1882-1904.
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