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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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