We are concerned with non-local parabolic equations in the presence of a divergence free drift term. By using the classical Nash approach, we show the existence of fundamental solutions together with continuity estimates, under weak regularity assumptions on the kernel of the non-local term and the velocity of the drift term. As an application, we give an alternative proof of global regularity for the two-dimensional dissipative quasi-geostrophic equations in the critical case.
- 2D dissipative quasi-geostrophic equations
- Divergence free drift
- Fundamental solutions
- Nash iteration
- Non-local parabolic equations
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