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Seminar

Research Seminar: On the stochastic NLS equation on compact Riemannian manifolds September 23, 2015 (11:30 AM PDT - 12:30 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Annie Millet (Université Paris I (Panthéon-Sorbonne))
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We show the existence and  uniqueness of a local maximal solution to stochastic nonlinear Schr\"odinger equations with multiplicative noise on a compact d-dimensional  Riemannian manifold. Our  approach uses a stochastic version of the Strichartz inequalities.

When d=2, we then give sufficient conditions to have a global solution in the focusing and defocusing cases. This is based on conservation laws; to prove them with a random perturbation, we need to  reformulate our NLS equation in terms of a Stratonovich integral, which requires more regularity on the driving noise and on the diffusion coefficient.

This is joint work with Z. Brzezniak.

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