中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

 

报告人Dr. Deng Zhang(Shanghai Jiao Tong University)

  目:Minimal mass blow-up solutions to rough nonlinear Schr?dinger equations

  间:2020.11.12(星期四), 16:00-17:00

  点:Tencent Meeting ID: 921 141 981 Password:123456

 要:In this talk we consider the focusing mass-critical rough nonlinear Schr?dinger equations, where the stochastic integration is taken in the sense of controlled rough path. In both dimensions one and two, the minimal mass blow-up solutions are constructed, which behave asymptotically like the pseudo-conformal blow-up solutions near the blow-up time. Moreover, the global well-posedness is obtained if the mass of the initial data is below that of the ground state. These results also yield that the mass of the ground state is exactly the threshold of global well-posedness and blow-up in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schr?dinger equations with lower order perturbations, in the absence of the pseudo-conformal symmetry and the conservation of energy. The talk is based on the joint work with Yiming Su.

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