Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space

We consider a stochastic nonlinear Schrödinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing Stochastic NLSE in H¹ on compact manifolds and bounded domains. We construct a martingale solution using a modified Faedo-Galerkin-method based on the Littlewood-Paley-decomposition. For 2d manifolds with bounded geometry, we use Strichartz estimates to show pathwise uniqueness.