MATH675

Introduction to tools of modern analysis which have been used in recent years in the study of partial differential equations: Fourier transform, Calderon-Zygmund theory, interpolation, Lebesgue spaces, Lorentz spaces, Sobolev spaces, Besov spaces, Littlewood-Paley theory, multipliers, Bernstein inequalities, the fractional Leibniz rule, Strichartz estimates, velocity averaging lemma. Applications to some of the following PDEs: the Navier-Stokes equations, Euler equations, nonlinear Schrodinger equations, nonlinear wave equations, the Patlak Keller Segel model.