Abstract
In this article we study the heat transfer equation with a supercritical diffusion term of an incompressible fluid in porous media governed by Darcy's law. We obtain the global well-posedness for small initial data belonging to critical Besov spaces and the local well-posedness for arbitrary initial data. We further show the pointwise blowup criterion.
Acknowledgements
The author would like to thank Prof. Changxing Miao for helpful comments and suggestions. The author is also grateful to the referees for valuable advice.