Regularity of solutions for the critical N-dimensional Burgers' equation

Chan, Chi Hin; Czubak, Magdalena

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 471-501

We consider the fractional Burgers' equation on ${ℝ}^N$ 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 $L^2\left({ℝ}^N\right)$.

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

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