On the wave turbulence theory for a random multidimensional KdV type equation
On the wave turbulence theory for a random multidimensional KdV type equation

Gigliola Staffilani, Massachusetts Institute of Technology
In this work we were interested in deriving the 3wave kinetic equation associated to a multidimensional KdV type initial value problem with weak bilinear interactions measured via a parameter \lambda with and without small noise. The main result states that such a kinetic equation can be derived unconditionally and for the expected interval of time of \lambda^2 when the physical dimension is high enough. We believe this is the first result in which the expected time scale has been achieved without any strong a priori assumption on the problem at hand. This is work with MinhBinh Tran.