Room 232
Amado Mathematics Building
Technion - Israel Institute of Technology
Haifa, Israel

Lecture I: June 4, 2001 (15:30)

Invariant measures for the Inviscid Burgers equation with periodic boundary conditions

The Burgers equation is the simplest dynamical system of the hydrodynamical type for which many questions concerning the statistics of solutions can be solved. In our joint papers with W. E, K. Khanin and A. Mazel we developed some general methods for attacking the basic problems which reveal new and beautiful connections with the theory of dynamical systems. The purpose of this lecture is to explain these methods, some results and several open problems.

Lecture II: June 6, 2001 (15:30)

Stationary distributions for the 2-D Navier-Stokes system and thermodynamical formalism

Three recently published independent papers (Kuksin and Shirikian; Kupiainen, Bricmont and Lefevre; E, Mattingly and Sinai) are based on the same idea and contain basically the same result on the uniqueness of the invariant measure for the 2-D Navier-Stokes system with random forcing. The purpose of the talk is to explain this idea and to outline the derivation of the result.

Lecture III: June 7, 2001 (15:30)

New finite-dimensional approximations of equations of hydrodynamical type

In this talk I shall explain our recent paper with Dinaburg and Posvyanskii. We simplify the nonlinear term so that the resulting equation is simpler but describes the same processes of development of singularities. The subject is controversial but definitely deserves some discussion