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

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.

33 pages

References in corpus (2)

• Travelling and rotating solutions to the generalized inviscid surface quasi-geostrophic equation
• Traveling vortex pairs for 2D incompressible Euler equations

Cited by in corpus (1)

• Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations