Multi-bubble Bourgain-Wang solutions to L2-critical nonlinear Schrödinger equation
A talk in the Bielefeld Stochastic Afternoon series by
Deng Zhang
| Abstract: | Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
This is a talk in the "Bielefeld Stochastic Afternoon" and the "Bielefeld Analysis Seminar".
In this talk, we are concerned with a general class of focusing mass-critical nonlinear Schrödinger equations with lower order perturbations, for which the pseudo- conformal symmetry and the conservation law of energy are absent. Two canonical examples are the deterministic nonlinear Schrödinger equations (NLS) and the stochastic nonlinear Schrödinger equation driven by the linear multiplicative noise. In dimensions one and two, we construct Bourgain-Wang type solutions, concentrating at finitely many distinct singularities, and prove that they are unique if the asymptotical behavior is within the order (𝑇 − 𝑡)4+, for t close to the blow-up time T. This provides examples for the mass quantization conjecture. In particular, through the pseudo-conformal transform, to the best of our knowledge, this provides the first examples of non-pure multi-solitons to L2-critical NLS. The talk is based on the work in joint with Michael Röckner and Yiming Su. Within the CRC this talk is associated to the project(s): A1, B1, B8 |