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Nonlinear Analysis

A new analytical approach to wave Turbulence

Jalal Shatah, Courant Institute

Location:  HILL 705
Date & time: Tuesday, 17 October 2017 at 1:40PM - 2:40PM

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.

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