Seminar| Institute of Mathematical Sciences
Time：Friday, October 28th, 2022, 15:30-16:45
Location：RS408, IMS; Online, Tecent Meeting
Speaker: Deng Zhang, Shanghai Jiaotong University
Abstract:In this talk we are mainly concerned with the dynamics of a general class of focusing mass-critical nonlinear Schrödinger equations (NLS) with lower order perturbations, for which the pseudo-conformal symmetry and the conservation law of energy can be absent. Two canonical examples are stochastic NLS driven by linear multiplicative noise and deterministic NLS. We show the construction of multi-bubble Bourgain-Wang type blow-up solutions, and the uniqueness in the energy class where the convergence rate is of the order (T-t)^{4+}. In the case of mass-critical NLS, the corresponding existence and conditional uniqueness of non-pure multi-solitons (including dispersive part) also will be presented. These results in particular provide new examples of mass quantization conjecture and soliton resolution conjecture. If time permits, I will also show the recent results on the refined uniqueness of multi-bubble blow-ups and multi-solitons for the mass-critical NLS.