On the global well-posedness of stochastic Schrödinger-Korteweg-de Vries system

2023/04/28 by Jie Chen, Chen, Jie, Fan Gu +3
Economics, Econometrics and Finance · Mathematics · #35Q53 #35Q55 #60H15 #Advanced Mathematical Physics Problems #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2304.14866

openalex publication_date 2023/04/28 · openalex created_date 2023/05/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the global well-posedness of the stochastic S-KdV system in H¹(ℝ)× H¹(ℝ), which are driven by additive noises. It is difficult to show the global well-posedness of a related perturbation system even for smooth datum and stochastic forces. To overcome it, we introduce a new sequence of approximation equations, which is the key of this paper. We establish priori estimates, global well-posedness and convergences of these approximation equations, which help us to get a pathwise priori estimate of the initial system.

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