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A free-boundary problem for Euler flows with constant vorticity on the sphere. (English) Zbl 1392.35217

Summary: A free-boundary problem for two-dimensional Euler flows with uniform vorticity on the surface of sphere is considered using the stereographic projection and the argument principle in complex variables. With the constant speed condition on the boundary, a circle turns out to be the unique solution on the sphere.

MSC:

35Q31 Euler equations
35R35 Free boundary problems for PDEs
76B47 Vortex flows for incompressible inviscid fluids
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