Stochastic nonlinear Schrödinger equations on tori

2018/03/07 by Cheung, Kelvin, Mosincat, Razvan
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1803.02817

Abstract

We consider the stochastic nonlinear Schrödinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness in L²(\mathbbT). As for other power-type nonlinearities, namely (i) (super)quintic when d = 1 and (ii) (super)cubic when d ≥ 2, we prove local well-posedness in all scaling-subcritical Sobolev spaces and global well-posedness in the energy space for the defocusing, energy-subcritical problems.

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