Regularity of solutions for the critical N-dimensional Burgers' equation
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, p. 471-501

We consider the fractional Burgers' equation on N 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 L 2 ( N ).

Nous considérons l'équation de Burgers avec diffusion fractionnelle dans N . Nous montrons l'existence de solutions globales regulières pour toute donnée initiale dans L 2 ( N ), en utilisant une version parabolique de la méthode de De Giorgi introduite par Caffarelli et Vasseur.

@article{AIHPC_2010__27_2_471_0,
     author = {Chan, Chi Hin and Czubak, Magdalena},
     title = {Regularity of solutions for the critical N-dimensional Burgers' equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {27},
     number = {2},
     year = {2010},
     pages = {471-501},
     doi = {10.1016/j.anihpc.2009.11.008},
     zbl = {1189.35354},
     mrnumber = {2595188},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 27 (2010) no. 2, pp. 471-501. doi : 10.1016/j.anihpc.2009.11.008. http://www.numdam.org/item/AIHPC_2010__27_2_471_0/

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