On 3-D vortex patches in bounded domains

Mathematics – Analysis of PDEs

Scientific paper

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34 pages

Scientific paper

This article concerns the equations of motion of perfect incompressible
fluids in a 3-D, smooth, bounded, simply connected domain. We suppose that the
curl of the initial velocity field is a vortex patch, and examine the classical
problems of the existence of a solution, either locally or globally in time,
and of the persistence of the initial regularity.

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