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arXiv · 2005.09154

Global solutions for a family of GSQG front equations

John K. Hunter·Jingyang Shu·Qingtian Zhang
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Abstract

We prove the global existence of solutions with small and smooth initial data of a nonlinear dispersive equation for the motion of generalized surface quasi-geostrophic (GSQG) fronts in a parameter regime $1<α<2$, where $α=1$ corresponds to the SQG equation and $α=2$ corresponds to the incompressible Euler equations. This result completes previous global well-posedness results for $0<α\le 1$. We also use contour dynamics to derive the GSQG front equations for $1<α<2$.

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John K. Hunter, Jingyang Shu, Qingtian Zhang. 2020-05-19. Global solutions for a family of GSQG front equations. https://arxiv.org/abs/2005.09154

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