In this paper we study the model of heat transfer in a porous medium with a critical diffusion. We obtain global existence and uniqueness of solutions to the equations of heat transfer of incompressible fluid in Besov spaces $\dot B^{3/p}_{p,1}(\mathbb{R}^3)$ with $1\le p\le\infty$ by the method of modulus of continuity and Fourier localization technique.
Ill-posedness of basic equations of fluid dynamics in Besov spaces
Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces
Local and global existence for the Lagrangian Averaged Navier-Stokes equations in Besov spaces
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