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

Abstract

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

31 pages; corrected one of the references, and fixed some typos

References in corpus (1)

• Blow up and regularity for fractal Burgers equation