Trevor Leslie : The Aubin-Lions-Simon Compactness Theorem

Posted by David Reynolds , part of the Graduate Analysis Seminar.

At

Nov. 29, 2017, 4 p.m.

In

SEO 512

Abstract

The Aubin-Lions Theorem, proved in the 1960s, is a useful tool for extracting subsequences (of Banach space-valued functions) which converge in some sense. For example, it is a key step in one of the standard proofs of the existence of weak solutions to the classical Navier-Stokes Equations, namely showing that a subsequence of the relevant Galerkin approximations converges to a solution. Later, Simon removed the hypothesis that the underlying Banach spaces must be reflexive. The resulting theorem is consequently sometimes called the Aubin-Lions-Simon Theorem. In this talk, we state and prove the Aubin-Lions-Simon Theorem. If time allows, we will give an application that requires Simon's version of the Theorem.