Analysis Seminar

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Out-Of-Equilibrium Dynamics for the Nonlinear Schrödinger Equation: From Energy Cascades to Weak Turbulence

Speaker: Zaher Hani, Courant

Location: Warren Weaver Hall 1302

Date: Thursday, September 19, 2013, 11 a.m.

Synopsis:

Out-of-equilibrium dynamics are a characteristic feature of the long-time behavior of nonlinear dispersive equations on bounded domains. This is partly due to the fact that dispersion does not translate into decay in this setting (in contrast to the case of unbounded domains like \(R^d\)). In this talk, we will take the cubic nonlinear Schrödinger equation as our model and discuss some results and aspects of this out-of-equilibrium dynamics, from energy cascades (i.e. migration of energy from low to high frequencies) to weak turbulence.