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

We focus on the regularity theory of two important equations of Fluid mechanics: the Euler equations and the Navier-Stokes equations in 2 and 3 dimensions. Some topics to be discussed: local regularity theory, regularity criteria, criticality and global solutions, the Leray weak solutions, the generalized SQG equations, global stability of certain steady solutions..