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

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

**Conferenciante:** Jaemin Park, U. de Barcelona

**Fecha:** Miércoles 4 de mayo de 2022 - 15:00

**Resumen:**In this talk, we study stationary solutions to the 2D incompressible Euler equations in the whole plane. It is well-known that any radial vorticity is stationary. For compactly supported vorticity, it is more difficult to see whether a stationary solution has to be radial. In the case where the vorticity is non-negative, it has been shown that any stationary solution has to be radial. By allowing the vorticity to change the sign, we prove that there exist non-radial stationary patch-type solutions. We construct patch-type solutions whose kinetic energy is infinite or finite. For the finite energy case, it turns out that a construction of a stationary solution with compactly supported velocity is possible.