|Location:||MSRI: Simons Auditorium|
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.No Notes/Supplements Uploaded No Video Files Uploaded