2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173627We 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 \cite{Driftdiffusion} and show existence of smooth solutions given any initial datum in $L^2(\R^N)$.31 pages; corrected one of the references, and fixed some typosAnalysis of PDEstext