Abstract. In this talk, I will discuss radial and one-dimensional symmetry properties for the stationary incompressible Euler equations in dimension 2 and some related semilinear elliptic equations. I will show that a steady flow of an ideal incompressible fluid with no stagnation point and tangential boundary conditions in an annulus is a circular flow. The same conclusion holds in complements of disks as well as in punctured disks and in the punctured plane, with some suitable conditions at infinity or at the origin. If possible, I will also discuss the case of parallel flows in two-dimensional strips, in the half-plane and in the whole plane. The proofs are based on the study of the geometric properties of the streamlines of the flow and on radial and one-dimensional symmetry results for the solutions of some elliptic equations satisfied by the stream function. The talk is based on joint works with N. Nadirashvili.

Bio. Professor François Hamel is a full professor of highest level at Aix-Marseille University in France. He was a former student of the Ecole Normale Supérieure in Paris. He received his PhD degree from Paris 6 University (now called Sorbonne University) in 1996, under the guidance of Professor Henri Berestycki. Before moving to Marseille in 2001, he was a CNRS researcher in Paris and a lecturer at MIT. He is an honorary member of the French Institut Universitaire de France and an honorary fellow of the German Alexander von Humboldt Foundation. He was included in the list of Highly Cited Researchers in 2014. He wrote more than 100 research papers on elliptic and parabolic partial differential equations, on propagation phenomena for reaction-diffusion equations, on shape optimization problems, and on theoretical aspects of population dynamics and biological invasions.