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On 3-d vortex patches in bounded domains. (English) Zbl 1030.76011
The article deals with Euler system for a perfect incompressible fluid in a smooth, bounded simply connected three-dimensional domain Ω. On the boundary one imposes the slip condition and one assumes that the curl of the initial velocity field v 0 is a vortex patch with some conormal smoothness implying v 0 Lip(Ω). The main results consist in proving the existence of solution, either locally or globally in time, and the persistence of initial regularity.
MSC:
76B47Vortex flows
35Q35PDEs in connection with fluid mechanics