Analysis and PDE Seminar: The stochastic nonlinear Schrödinger equations: defocusing mass and energy critical cases

Seminar | October 7 | 4:10-5 p.m. | 939 Evans Hall

 Deng Zhang, SJTU

 Department of Mathematics

In this talk we will present our recent results on stochastic nonlinear Schrödinger equations with linear multiplicative noise, particularly, in the defocusing mass-critical and energy-critical cases. More precisely, for general initial data, we obtain the global existence and uniqueness of solutions in both mass-critical and energy-critical case. When the quadratic variation of noise is globally bounded, we also prove the rescaled scattering behavior of stochastic solutions in the spaces L2, H1 as well as the pseudo-conformal space. Furthermore, the Stroock-Varadhan type theorem is derived for the topological support of solutions to stochastic nonlinear Schrödinger equations in the Strichartz and local smoothing spaces.