Seminars & Colloquia Calendar

Abstract:  Weak turbulence is the non-equilibrium statistical mechanics of weakly non-linear waves.  The most attractive feature of the theory of wave turbulence, as it has developed since the 60’s, is the derivation of a kinetic equation, known as the kinetic wave equation. In this talk I will consider wave turbulence theory for the nonlinear Schrodinger equation on a torus of size L and for solutions of size $\varepsilon$.  I will discuss the long time dynamics of solutions as $\varepsilon \rightarrow 0$ (weak nonlinearity) and L ,  $\rightarrow \infty$  (large box limit).  I will also discuss the latest advances on deriving the kinetic equation.