ACDC Seminar by Taoufik Hmidi on the 2nd of December

On the 2nd of December at 15.00, Taoufik Hmidi will give an Amsterdam Dynamics Seminar. We will go for drinks at Bar Boele after the talk.

The talk will take place in the Maryam seminar room (9A-46).

Title:
Rigid Time-Periodic Solutions of the Euler Equations: Rigidity, Flexibility, and Bifurcation

Abstract:

In this talk, I will present an overview of recent developments concerning rigidly rotating solutions of the two-dimensional incompressible Euler equations, with particular emphasis on vortex patches and the interplay between rigidity and flexibility.

On the rigidity side, I will explain how techniques from potential theory, variational methods, and complex analysis can be combined to characterize rotating vortex patches in certain parameter regimes and establish uniqueness results.

On the flexibility side, I will discuss the existence of nontrivial families of rotating vortex patches arising through bifurcation in infinite-dimensional function spaces. Particular attention will be devoted to bifurcations from the disc and the annulus, illustrating the rich structure of both simply and doubly connected rotating patches.

Finally, I will outline some recent developments and perspectives on the construction of time-quasi-periodic vortex patches using KAM theory.

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