On the V-states for some transport models

On the V-states for some transport models

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Zineb Hassainia , New York University
Fine Hall 322

We shall discuss in this talk some aspects of the vortex motion for different nonlinear transport models arising in fluid dynamics such as Euler equations and the inviscid generalized surface quasi-geostrophic equations. The main concern is to establish the existence of rotating vortex patches (also called V-states) for different topological structures: simply connected and doubly connected patches. The proofs are based on the bifurcation theory combined with special functions.The existence of the V-states in a disc and their interaction with the boundary will also be analyzed. The content of this lecture is based on joint papers with de-La Hoz, Hmidi and Mateu.