Thursday, July 23, 2020 - 12:30 in ZOOM - Video Conference
Minimal mass blow-up solutions to rough nonlinear Schrödinger equations
A talk in the Cluster Group Stochastic Analysis series by
Deng Zhang from Shanghai Jiao Tong University
| Abstract: |
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
In this talk we consider the focusing mass-critical rough nonlinear Schrödinger equations, where the stochastic integration is taken in the sense of controlled rough path.
We obtain the global well-posedness if the mass of initial data is below that of the ground state.
Moreover, the minimal mass blow-up solutions are also constructed in both dimensions one and two.
In particular, these results yield that the mass of the ground state is exactly the threshold of global well-posedness and blow-up of solutions in the stochastic case.
The proof is mainly based on the rescaling approach and the modulation method recently developed by Raphaël and Szeftel.
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