Wednesday, September 25, 2019 - 15:00 in X-E0-002
Behavior of solutions in stochastic critical and supercritical NLS equation with additive or multiplicative noise
A talk in the Keine Reihe series by
Annie Millet from Université Paris 1 Panthéon-Sorbonne
| Abstract: |
We study nonlinear Schrödinger (NLS) equation with focusing nonlinearity, subject to additive or multiplicative stochastic perturbations driven by an infinite dimensional Brownian motion.
Under the appropriate assumptions on the space covariance of the driving noise, previously A.~de Bouard and A.~Debussche established the $H^1$ local well-posedness in a general case and global well-posedness in the mass-subcritical case.
In our work we study the $L^2$-critical, intercritical and energy ($\dot{H}^1$)-critical cases of stochastic NLS, and obtain quantitative estimates on the blow-up time when the mass, energy and $L^2$-norm of the gradient of the initial condition are controlled by similar quantities of the ground state.
This is joint work with Svetlana Roudenko.
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