Student Probability Seminar

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Invariant Gibbs Measures for Nonlinear Schrodinger Equation

Speaker: Partha Dey

Location: Warren Weaver Hall 202

Date: Friday, April 22, 2011, 4:30 p.m.

Synopsis:

Nonlinear Schrodinger equations (NLS) idealistically model the dynamics of complex-valued functions arising in complex phenomena such as Langmuir waves in Plasma, laser field in nonlinear medium etc. The Hamiltonian is unbounded below and under certain circumstances solutions can develop singularities in finite time. First we will survey existing results about the existence of solutions and their behavior. We will then show how to use simple probabilistic arguments to prove existence of invariant Gibbs measure (for radial functions on unit disc in any dimension) in the subcritical region where singularities cannot form.