Display Abstract

Title Qualitative properties of maximal entropy solutions for 2D Euler's equation

Name Juraj Foldes
Country USA
Email foldes@ima.umn.edu
Co-Author(s) Vladimir Sverak
Submit Time 2014-02-28 11:16:50
Special Session 60: Recent advances in evolutionary equations
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.