Online Analysis and PDE seminar (UAM-UC-UC3M-UCM-ICMAT-IMUS)

Conferenciante: David Ruiz, Universidad de Granada

Fecha: Miércoles 23 de marzo de 2022 - 15:00

Enlace al seminario

Resumen: In this talk we present some recent results regarding compactly supported solutions of the 2D steady Euler equations. Under some assumptions on the support of the solution, we prove that the streamlines of the flow are circular. The proof uses that the corresponding stream function solves an elliptic semilinear problem. One of the main difficulties in our study is that the nonlinear term can fail to be Lipschitz continuous near the boundary values.

 

In some cases we can apply a local symmetry result of F. Brock to conclude. Otherwise, we are able to use the moving plane scheme to show symmetry, despite the possible lack of regularity of the nonlinear term. We think that such result is interesting in its own right and will be stated and proved also for higher dimensions. The proof requires the study of maximum principles, Hopf lemma and Serrin corner lemma for elliptic linear operators with singular coefficients.