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

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

2008-10-17

arxiv.org/abs/0810.3055v3

Mathematics

Analysis of PDEs

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

Scientific paper

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 $L^2(\R^N)$.

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