Regularity of solutions for the critical N-dimensional Burgers' equation
Chi Hin Chan
Department of Mathematics, The University of Texas at Austin, 1 University Station C1200 Austin, TX 78712-0257, USAMagdalena Czubak
Department of Mathematics, University of Toronto, 40 St. George St. Toronto, Ontario, M5S 2E4, Canada
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Abstract
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 .
Résumé
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.
Cite this article
Chi Hin Chan, Magdalena Czubak, Regularity of solutions for the critical N-dimensional Burgers' equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 2, pp. 471–501
DOI 10.1016/J.ANIHPC.2009.11.008