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

Source 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 $L^2(\mathbb{T})$.