• Lecturer: László Székelyhidi
• Date: Thursday and Friday 09:00 - 11:00
• Room: University SG 3-11
• Language: German or English
• Target audience: MSc students, Diploma students, PhD students, Postdocs
• Keywords: Geoemtric group theory, growth of groups, topologial group theory
• Prerequisites: The course does not require any previous knowledge of fluid mechanics or familiarity with the Navier-Stokes equations, but some previous experience with PDE is strongly recommended.

Abstract:

The Navier-Stokes equations, governing the motion of an incompressible viscous fluid, are derived based on certain physical assumptions concerning the motion of the fluid. In the words of J.Leray in 1934, "these hypothesis need to be justified a posteriori by establishing the following existence theorem: there is a solution which corresponds to a state of velocity given arbitrarily at an initial instant" This problem, although still without answer 85 years later, inspired a wealth of mathematical development, the introduction of many different notions of solutions (classical, weak, mild, suitable,...) and different approaches (fixed point methods, energy methods, blow-up arguments,...). In the lectures we will give an overview of these different directions, mainly focussing on the theory of weak solutions introduced by Leray and Hopf, including such topics as (i) existence, (ii) partial regularity, and (iii) criteria for uniqueness and regularity.