摘要
In this paper, we study the existence and qualitative properties of multiscale steady vortex patches for Euler equations in a 2D bounded domain. By considering certain maximization problems for the vorticity, we obtain the existence of double vortex patches which are trapped in a neighborhood of two points. Limiting localizations of these two points are determined by the Robin function and the boundary of the domain, rather than critical points of the Kirchhoff-Routh function H2, which is quite different from all the known results. Moreover, the strengths of two components of vorticity are of different order. Multiscale vortex patches concentrating near k points are also constructed for any integer k ≥ 2.
源语言 | 英语 |
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页(从-至) | 1488-1514 |
页数 | 27 |
期刊 | SIAM Journal on Mathematical Analysis |
卷 | 54 |
期 | 2 |
DOI | |
出版状态 | 已出版 - 2022 |