| Abstract: |
| We prove local well posedness for the focusing/defocusing stochastic NLS equation in dimension 3 to 5 for an $H^1$-critical nonlinearity and an additive/multiplicative stochastic perturbation.
In the case of a focuslng nonlinearity, we give criteria on the initial condition to obtain either some quantitative information about the maximal existence time, or blow-up with positive probability. |
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