Probability Seminar——Recent results on stochastic nonlinear Schr?dinger and Zakharov equations
报告人：张登（上海交通大学）
时间：2025-05-12 14:00-15:00
地点：智华楼-四元厅
Abstract：In this talk we will review some recent results on stochastic nonlinear Schr?dinger and Zakharov equations. We will first consider the focusing mass-critical nonlinear Schr?dinger equations in both the stochastic and deterministic case, and show the construction and conditional uniqueness of multi-bubble Bourgain-Wang type blow-up solutions and non-pure multi-solitons. In the low asymptotic regime, the refined uniqueness is derived as well.
Furthermore, we consider the stochastic Zakharov system, which couples the Schroedinger and wave equations, and reaches the energy criticality in dimension four. We will show the global well-posedness below the ground state and the noise regularization effects on blow-up and scattering dynamics.
