Some variants of the Aubin-lions lemma

Abstract

The purpose of this thesis is to write out and extend the paper [Mou16] by Ayman Moussa, which provides a modern approach to the classical Aubin-Lions Lemma. The author of [Mou16] states and proves in his work two generalizations of the Aubin-Lions Lemma, which is an in- dispensable tool in the studies of nonlinear parabolic differential equations. The two versions handle the problems, delivered by the estimates of degenerated evolution equations and in- compressible Navier-Stokes equations, the latter being considered on a non-cylindrical domain. The interesting fact about his work is his totally different approach to these problems, which where already studied by many other authors, without using the Aubin-Lions Lemma itself. We prepare appropriate theory, use most of the ideas and strategies of [Mou16] and carry out the proofs in [Mou16] substantially equal.