Monday, June 3, 2024 - 17:00 in V2-210/216
Pathwise well-posedness of stochastic nonlinear dispersive equations with multiplicative noises
A talk in the Harmonic and Stochastic Analysis of Dispersive PDEs series by
Andreia Chapouto from University of Edinburgh
| Abstract: |
Over the last decades, the well-posedness issue of stochastic dispersive PDEs with multiplica-
tive noises has been extensively studied. However, this comes mostly from the viewpoint
of Ito solution theory, and pathwise well-posedness remains completely open. In this talk,
I will present the first pathwise well-posedness results for stochastic nonlinear wave equa-
tions (SNLW) and stochastic nonlinear Schrödinger equations (SNLS) with multiplicative
white-in-time/coloured-in-space noise. In proving pathwise well-posedness, we combine the
operator-value controlled rough paths adapted to dispersive flows, together with random tensor
estimates, and the Fourier restriction norm method adapted to controlled rough paths.
|
Back
