Infinite volume limit for the Nonlinear Schrodinger Equation and Weak turbulence

Infinite volume limit for the Nonlinear Schrodinger Equation and Weak turbulence

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Pierre Germain , NYU
Fine Hall 322

The theory of weak turbulence has been put forward by applied mathematicians to describe the asymptotic behavior of NLS set on a compact domain - as well as many other infinite dimensional Hamiltonian systems. It is believed to be valid in a statistical sense, in the weakly nonlinear, infinite volume limit. I will present how these limits can be taken rigorously, and give rise to new equations.