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arXiv · 2103.03992

Existence and regularity of co-rotating and travelling global solutions for the generalized SQG equation

Daomin Cao·Guolin Qin·Weicheng Zhan·Changjun Zou
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Abstract

By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and travelling global solutions for the gSQG equation, which extends the result of Hmidi and Mateu \cite{HM} to $\alpha\in[1,2)$. Moreover, we prove the $C^\infty$ regularity of vortices boundary, and show the convexity of each vortices component.

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Daomin Cao, Guolin Qin, Weicheng Zhan, Changjun Zou. 2021-03-06. Existence and regularity of co-rotating and travelling global solutions for the generalized SQG equation. https://arxiv.org/abs/2103.03992

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