On the V-states for the generalized quasi-geostrophic equations

Abstract

We prove the existence of the V-states for the generalized inviscid SQG equations with $\alpha \in ]0,1[.$ These structures are special rotating simply connected patches with $m-$ fold symmetry bifurcating from the trivial solution at some explicit values of the angular velocity. This produces, inter alia, an infinite family of non stationary global solutions with uniqueness.

arXiv comment54 pages

References in corpus (1)

• Boundary regularity of rotating vortex patches

Cited by in corpus (11)

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• Imperfect bifurcation for the quasi-geostrophic shallow-water equations
• Strong illposedness for SQG in critical Sobolev spaces
• Global bifurcation for corotating and counter-rotating vortex pairs
• Existence of small loops in the Bifurcation diagram near the degenerate eigenvalues
• Vortex patches choreography for active scalar equations
• Existence and stability of smooth traveling circular pairs for the generalized surface quasi-geostrophic equation
• Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation