Global existence for some transport equations with nonlocal velocity

Abstract

In this paper, we study transport equations with nonlocal velocity fields with rough initial data. We address the global existence of weak solutions of an one dimensional model of the surface quasi-geostrophic equation and the incompressible porous media equation, and one dimensional and $n$ dimensional models of the dissipative quasi-geostrophic equations and the dissipative incompressible porous media equation.

Submitted on May 21st, 2014

References in corpus (1)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation