Invariant Measures for the derivative nonlinear Schrödinger equation
Vortrag von Dr. Giuseppe Genovese Datum: 24.04.17 Zeit: 09.30 - 10.15 Raum: Y27H46
The derivative nonlinear Schrödinger equation (DNLS) is a dispersive nonlinear PDE coming from magnetoidrodynamics. It is an integrable system, in the sense that there is an infinite sequence of integrals of motion, conserved by the flow for sufficiently regular solutions. I will show how to construct a family of invariant Gibbs measures associated to the integral of motions, when the L^2 norm of the solution is sufficiently small. This construction makes the DNLS an infinite dimensional (Hamiltonian) dynamical system, in a regime where some form of ergodicity (to be further investigated) is expected to hold.