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

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

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Gigliola Staffilani, Massachusetts Institute of Technology

In this work we were  interested in deriving the 3-wave 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 Minh-Binh Tran.