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arXiv · 1404.5039

Stochastic nonlinear Schrödinger equations

Viorel Barbu·Michael Röckner·Deng Zhang
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Abstract

This paper is devoted to the well-posedness of stochastic nonlinear Schrödinger equations in the energy space H1(Rd), which is a natural continuation of our recent work [1]. We consider both focusing and defocusing nonlinearities and prove global well-posedness in H1(Rd), including also the pathwise continuous dependence on initial conditions, with exponents exactly the same as in the deterministic case. In particular, this work improves earlier results in [4]. Moreover, the local existence, uniqueness and blowup alternative are also established for the energy-critical case. The approach presented here is mainly based on the rescaling approach already used in [1] to study the L2 case and also on the Strichartz estimates established in [12] for large perturbations of the Laplacian.

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Viorel Barbu, Michael Röckner, Deng Zhang. 2014-04-20. Stochastic nonlinear Schrödinger equations. https://arxiv.org/abs/1404.5039

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