Nous considérons l'équation de Burgers avec diffusion fractionnelle dans . Nous montrons l'existence de solutions globales regulières pour toute donnée initiale dans , en utilisant une version parabolique de la méthode de De Giorgi introduite par Caffarelli et Vasseur.
We consider the fractional Burgers' equation on with the critical dissipation term. We follow the parabolic De-Giorgi's method of Caffarelli and Vasseur and show existence of smooth solutions given any initial datum in .
@article{AIHPC_2010__27_2_471_0, author = {Chan, Chi Hin and Czubak, Magdalena}, title = {Regularity of solutions for the critical {\protect\emph{N}-dimensional} {Burgers'} equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {471--501}, publisher = {Elsevier}, volume = {27}, number = {2}, year = {2010}, doi = {10.1016/j.anihpc.2009.11.008}, mrnumber = {2595188}, zbl = {1189.35354}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.008/} }
TY - JOUR AU - Chan, Chi Hin AU - Czubak, Magdalena TI - Regularity of solutions for the critical N-dimensional Burgers' equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 471 EP - 501 VL - 27 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.008/ DO - 10.1016/j.anihpc.2009.11.008 LA - en ID - AIHPC_2010__27_2_471_0 ER -
%0 Journal Article %A Chan, Chi Hin %A Czubak, Magdalena %T Regularity of solutions for the critical N-dimensional Burgers' equation %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 471-501 %V 27 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.008/ %R 10.1016/j.anihpc.2009.11.008 %G en %F AIHPC_2010__27_2_471_0
Chan, Chi Hin; Czubak, Magdalena. Regularity of solutions for the critical N-dimensional Burgers' equation. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 471-501. doi : 10.1016/j.anihpc.2009.11.008. http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.008/
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