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

Abstract

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 ${\dot{B}}_{p,1}^{3/p}({\mathbb{R}}^3)$ with $1\le p\le \infty$ by the method of modulus of continuity and Fourier localization technique.

arXiv comment18 pages

References in corpus (3)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Global well-posedness of the critical Burgers equation in critical Besov spaces
• On the global well-posedness of the critical quasi-geostrophic equation