PERIODIC STOCHASTIC KORTEWEG–DE VRIES EQUATION WITH ADDITIVE SPACE-TIME WHITE NOISE

Abstract

We prove the local well-posedness of the periodic stochastic Korteweg–de Vries equation with the additive space-time white noise. To treat low regularity of the white noise in space, we consider the Cauchy problem in the Besov-type space(Formula Presented) such that sp (Formula Presented). In establishing local well-posedness, we use a variant of the Bourgain space adapted to (Formula Presented) and establish a nonlinear estimate on the second iteration on the integral formulation. The deterministic part of the nonlinear estimate also yields the local well-posedness of the deterministic KdV in M.(T), the space of finite Borel measures on T.