Topics in Differential Equations: Local and global regularity of nonlinear evolution equations

We focus on several basic questions concerning the dynamics of solutions of evolution equations. The main topics to be discussed are local regularity, global regularity, regularity criteria, and asymptotic stability of stationary solutions. While many examples are possible, we are mostly interested in these topics in the context of plasma models, such as the Vlasov-Poisson and the Vlasov-Maxwell systems.