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Session S37 - New Developments in Mathematical Fluid Dynamics

Thursday, July 15, 14:00 ~ 14:25 UTC-3

On the stationary and uniformly rotating solutions of the 2D Euler equation

Jaemin Park

Georgia Institute of Technology, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we discuss whether all stationary solutions of 2D Euler equation must be radially symmetric, if the vorticity is compactly supported or has some decay at infinity. Our main result is that for any non-negative smooth stationary vorticity that is compactly supported (or has certain decay as |x|->infty), it must be radially symmetric up to a translation. We have also obtained some symmetry results for uniformly-rotating solutions for 2D Euler equation. The symmetry results are mainly obtained by calculus of variations and elliptic equation techniques. This is a joint work with Javier Gomez-Serrano, Jia Shi and Yao Yao.

Joint work with Javier Gomez-Serrano (University of Barcelona, Spain), Jia Shi (Princeton University, United States) and Yao Yao (Georgia Institute of Technology, United States).

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