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 Ìýinterested in deriving the 3-wave kinetic equation associatedÌý to a multidimensional KdV type initial value problem with weak bilinear interactions measured via a parameter \lambda with and without Ìýsmall noise. The main resultÌýstates that such a kinetic equation can be derivedÌý ÌýÌýunconditionally and for the expected interval of time ofÌý \lambda^2 whenÌý 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 Ìýwork with Minh-Binh Tran.Ìý