The well-posedness of the stochastic nonlinear Schrödinger equations in H²(ℝ^d)

2022/05/06 by Dôku, Isamu, Hashimoto, Shunya, Machihara, Shuji
#35B65 #35J10 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2205.03095

Abstract

The Cauchy problem for the stochastic nonlinear Schrödinger equation with multiplicative noise is considered where the nonlinear term is of power type and the noise coefficients are purely imaginary numbers. The main purpose of this paper is to construct classical solutions in H²(ℝ^d) for the problem. The techniques of Kato \citeK87,K89 work well in overcoming this difficulty even for the stochastic equations.

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