Time evolution of a singular vortex patch. (Evolution temporelle d’une poche de tourbillon singulière.) (French) Zbl 0882.35093

The paper deals with the persistence of certain types of degenerated geometries for the 2d incompressible Euler system. One demonstrates that the zones where the field of the velocity is not a Lipschitz field does not contaminate the regular zones. The author proves the persistence of conormal regularity apart from a closed subset. As a consequence one gives the following result for the vortex patches: if the initial boundary is regular apart from a closed subset, it remains regular at any time apart from the closed subset transported by the flow.


35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
76B47 Vortex flows for incompressible inviscid fluids
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