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

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

2008-08-22

arxiv.org/abs/0808.3051v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

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.

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