Well-posedness and blowup criterion of generalized porous medium equation in Besov spaces

Abstract

We study the generalized porous medium equation of the form $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$ where P is an abstract operator. We obtain the local well-posedness in Besov spaces for large initial data, and show the solution becomes global if the initial data is small. Also, we prove a blowup criterion for the solution.

Keywords

• Generalized porous medium equation
• well-posedness
• blowup criterion
• Besov spaces