Existence and uniqueness of weak solutions to quasilinear PDEs with critical data

Abstract

We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when the initial data is merely bounded.

20 pages. Compared to version 2, the proof of Prop. 3.4(d) is updated and Rem. 3.7 removed