Regularity of solutions for the critical N-dimensional Burgers' equation
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🧮 math.AP
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burgerscriticalequationsolutionscaffarelliciteconsiderdatum
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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 $L^2(\R^N)$.
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