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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.