Regularity of solutions for the critical $N$-dimensional Burgers' equation
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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 \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 typos
31 pages; corrected one of the references, and fixed some typos