On the Energy of Inviscid Singular Flows
نویسنده
چکیده
ABSTRACT. It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space B 3,∞. When the singular set of the solution is (or belongs to) a smooth manifold, we derive various L-space regularity criteria dimensionally equivalent to the critical one. In particular, if the singular set is a hypersurface the energy of u is conserved provided the one sided non-tangential limits to the surface exist and the non-tangential maximal function is L integrable, while the maximal function of the pressure is
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