Espaces critiques pour le système des equations de Navier-Stokes incompressibles
| dc.creator | Auscher, Pascal | |
| dc.creator | Tchamitchian, Philippe | |
| dc.date | 2008-12-05 | |
| dc.date | 2008-12-30 | |
| dc.date.accessioned | 2026-07-07T12:22:38Z | |
| dc.date.available | 2026-07-07T12:22:38Z | |
| dc.description | In this work, we exhibit abstract conditions on a functional space E who insure the existence of a global mild solution for small data in E or the existence of a local mild solution in absence of size constraints for a class of semi-linear parabolic equations, which contains the incompressible Navier-Stokes system as a fundamental example. We also give an abstract criterion toward regularity of the obtained solutions. These conditions, given in terms of Littlewood-Paley estimates for products of spectrally localized elements of $E$, are simple to check in all known cases: Lebesgue, Lorents, Besov, Morrey... spaces. These conditions also apply to non-invariant spaces E and we give full details in the case of some 2-microlocal spaces. The following comments did not show on the first version: This article was written around 1998-99 and never published, because at that time, Koch and Tataru announced their result on well-posedness of Navier-stokes equations with initial data in $BMO^{-1}$. We believe though that some results and counterexamples here are of independent interest and we make them available electronically. | |
| dc.description | No modification to the text. This work was done when the first author was at Université de Picardie | |
| dc.identifier | https://arxiv.org/abs/0812.1158 | |
| dc.identifier | http://arxiv.org/abs/0812.1158 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213716 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 35K55, 35Q30, 35R05, 35S50, 42B25 | |
| dc.title | Espaces critiques pour le système des equations de Navier-Stokes incompressibles | |
| dc.type | text |