Dans cet article, nous montrons que les solutions faibles de l'équation quasi-géostrophique légèrement sur-critique deviennent régulières en temps grand. La démonstration utilise des idées d'un article récent de Caffarelli et Vasseur et repose sur un argument de type de De Giorgi.
We prove that weak solutions of the slightly supercritical quasi-geostrophic equation become smooth for large time. The proof uses ideas from a recent article of Caffarelli and Vasseur and is based on an argument in the style of De Giorgi.
@article{AIHPC_2010__27_2_693_0, author = {Silvestre, Luis}, title = {Eventual regularization for the slightly supercritical quasi-geostrophic equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {693--704}, publisher = {Elsevier}, volume = {27}, number = {2}, year = {2010}, doi = {10.1016/j.anihpc.2009.11.006}, mrnumber = {2595196}, zbl = {1187.35186}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.006/} }
TY - JOUR AU - Silvestre, Luis TI - Eventual regularization for the slightly supercritical quasi-geostrophic equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 693 EP - 704 VL - 27 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.006/ DO - 10.1016/j.anihpc.2009.11.006 LA - en ID - AIHPC_2010__27_2_693_0 ER -
%0 Journal Article %A Silvestre, Luis %T Eventual regularization for the slightly supercritical quasi-geostrophic equation %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 693-704 %V 27 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.006/ %R 10.1016/j.anihpc.2009.11.006 %G en %F AIHPC_2010__27_2_693_0
Silvestre, Luis. Eventual regularization for the slightly supercritical quasi-geostrophic equation. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 693-704. doi : 10.1016/j.anihpc.2009.11.006. http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.006/
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