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Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type. (English) Zbl 0938.35128

The author proves a uniqueness theorem for the Euler equations for an ideal incompressible fluid assuming that the vorticity belongs to a Besov space. For obtaining a priori estimates one uses the wavelet decomposition of the vorticity. In the last part of the paper one proves an existence theorem in dimension two.

MSC:

35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76B47 Vortex flows for incompressible inviscid fluids
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