On a parabolic logarithmic Sobolev inequality
| dc.creator | Ibrahim, H. | |
| dc.creator | Monneau, R. | |
| dc.date | 2009-03-08 | |
| dc.date.accessioned | 2026-07-07T12:50:23Z | |
| dc.date.available | 2026-07-07T12:50:23Z | |
| dc.description | In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) $BMO$ norm. In this paper, we show a parabolic version of the Kozono-Taniuchi inequality by means of anisotropic (parabolic) $BMO$ norm. More precisely we give an upper bound for the $L^{\infty}$ norm of a function in terms of its parabolic $BMO$ norm, up to a logarithmic correction involving its norm in some Sobolev space. As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems. | |
| dc.identifier | https://arxiv.org/abs/0903.1436 | |
| dc.identifier | http://arxiv.org/abs/0903.1436 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222669 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 42B35; 54C35; 42B25; 39B05 | |
| dc.title | On a parabolic logarithmic Sobolev inequality | |
| dc.type | text |