Existence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equation

[摘要] By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and traveling-wave vortex solutions for the gSQG equation, which extends the result of Hmidi and Mateu [28] to alpha is an element of [1, 2). Moreover, we obtain the C-infinity regularity of vortices boundary and the convexity of each vortices component. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-25