Work

Normal form approach to unconditional well-posedness of the periodic stochastic Korteweg-de Vries equation with an additive noise

Year: 2026

Type: preprint

Abstract: We develop a stochastic normal form method for stochastic dispersive equations. As a model example, we study the stochastic Korteweg-de Vries equation (SKdV) with an additive noise, posed on the circle. By replacing integration by parts (in time) in the deterministic setting with Ito's product formula in the current stochastic setting, we transform SKdV with an additive noise into a stochastic normal form equation with additive and multiplicative noises. We then use the stochastic normal form equation to prove optimal pathwise unconditional global well-posedness of SKdV in $L^2(\mathbb{T})$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29935

Authors: Greco, Damiano, Oh, Tadahiro, Sosoe, Philippe, Wang, Yuzhao

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: The Supreme Challenges of Supremal Functionals, G2051586644, Probabilistic study of nonlinear Schrödinger equations on compact domains, Bi-parameter paracontrolled approach to singular stochastic wave equations, CAREER: Probability and Mathematical Statistical Mechanics, Fluctuations in Polymers and Random Data Partial Differential Equations

OpenAlex ID: W7223230047

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