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

We prove the local well-posedness of the periodic stochastic Koreweg-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 Besove-type space (b) over cap (s)(p,infinity)(T) for s = -1/2+, p = 2+ such that sp < -1. In establishing local well-posedness, we use a variant of the Bourgain space adapted to <(b)over cap>(s)(p,infinity)(T) 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.