On the stochastic nonlinear Schrödinger equation
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Mon, 25/10/2010 14:15 |
Annie Millet |
Stochastic Analysis Seminar  |
Eagle House |
| We consider a non linear Schrödinger equation on a compact manifold of dimension d subject to some multiplicative random perturbation. Using some stochastic Strichartz inequality, we prove the existence and uniqueness of a maximal solution in H^1 under some general conditions on the diffusion coefficient. Under stronger conditions on the noise, the nonlinearity and the diffusion coefficient, we deduce the existence of a global solution when d=2. This is a joint work with Z. Brzezniak. | |||