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

TL;DR

This paper proves the global existence and uniqueness of solutions for heat transfer in incompressible porous media with critical diffusion, using advanced mathematical techniques in Besov spaces.

Contribution

It establishes the well-posedness of the model in Besov spaces, extending previous results to a critical diffusion setting.

Findings

Global existence of solutions in Besov spaces

Uniqueness of solutions for the model

Application of modulus of continuity and Fourier localization methods

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