Math 828: Advanced Topics in Harmonic Analysis

We will discuss equations of fluid mechanics, in particular Navier-Stokes, Euler and surface quasi-geostrophic equations. We will start with an introduction covering basic existence and uniqueness questions, and proceed to discuss main directions of research. Some of the results we will talk about are fairly recent. Files of papers we will touch upon will be posted below (when available).

N. Katz and N. Pavlovic, "A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyperdissipation", pdf, GAFA Vol 12, 2002, 355--379.

A. Kiselev and F. Nazarov, "A simple energy pump for the periodic 2D QGE", pdf

S. Denisov, "Infinite superlinear growth of the gradient for the two-dimensional Euler equation", ps

P. Constantin, "The Euler equations and nonlocal conservative Ricatti equations", pdf, IMRN (2000), No 9, p. 455--465