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Regularity of solutions for the critical $$N$$-dimensional Burgers’ equation. (English) Zbl 1189.35354
Summary: 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 and show existence of smooth solutions given any initial datum in $$L^2(\mathbb R^N)$$.

##### MSC:
 35R11 Fractional partial differential equations 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs 86A05 Hydrology, hydrography, oceanography 35B45 A priori estimates in context of PDEs 35D30 Weak solutions to PDEs
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