On the energy of inviscid singular flows

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:349

Article

Shvydkoy, Roman

关键词: Euler equation;    Weak solutions;    Energy conservation;    Onsager conjecture;    Vortex sheets;   

DOI  :  10.1016/j.jmaa.2008.09.007

来源: Elsevier

【 摘 要 】

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.infinity)(1/3). When the singular set of the solution is (or belongs to) a smooth manifold, we derive various L(p)-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(3) integrable. while the maximal function of the pressure is L(3/2) integrable. The results directly apply to prove energy conservation of the classical vortex sheets in both 2D and 3D at least in those cases where the energy is finite. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free