On the energy of inviscid singular flows
| dc.creator | Shvydkoy, Roman | |
| dc.date | 2008-03-13 | |
| dc.date.accessioned | 2026-07-07T09:26:48Z | |
| dc.date.available | 2026-07-07T09:26:48Z | |
| dc.description | 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 $B^{1/3}_{3,\infty}$. 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. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0803.2056 | |
| dc.identifier | http://arxiv.org/abs/0803.2056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156884 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 76F02 (Primary); 76B47 (Secondary) | |
| dc.title | On the energy of inviscid singular flows | |
| dc.type | text |