Alexander Kiselev
Published 2010-09-02Version 1
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow up in the supercritical regime.
On the regularity of a class of generalized quasi-geostrophic equations
Regularity of n/2-harmonic maps into spheres
Everywhere regularity of certain types of parabolic systems
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