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In this paper we study the model of heat transfer in a porous medium with acritical diffusion. We obtain global existence and uniqueness of solutions tothe equations of heat transfer of incompressible fluid in Besov spaces $\dotB^{3/p}_{p,1}(\mathbb{R}^3)$ with $1\le p\le\infty$ by the method of modulus ofcontinuity and Fourier localization technique.

Global well-posedness of incompressible flow in porous media with critical diffusion in Besov spaces