Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 5.11.2015 at 14:00 Lecture room M-223

Juraj Foldes (Universite libre de Bruxelles):

Maximal entropy approach to dynamics of 2D Euler equation

Abstract:

Two dimensional turbulent flows for large Reynold's numbers can be approximated by solutions of incompressible Euler's equation.

As time increases, the solutions of Euler's equation are increasing their disorder; however, at the same time, they are limited by the

existence of infinitely many invariants. Hence, it is natural to assume that the limit profiles are functions which maximize an entropy

given the values of conserved quantities. Such solutions are described by methods of Statistical Mechanics and are called maximal

entropy solutions. Nevertheless, there is no general agreement in the literature on what is the right notion of the entropy.

We will show that on symmetric domains, independently of the choice of entropy, the maximal entropy solutions with small energy

respect the geometry of the domain.

This is a joint work with Vladimir Sverak (University of Minnesota).