Periodic Stochastic Korteweg-de Vries Equation

Details Periodic Stochastic Korteweg-de Vries Equation Periodic Stochastic Korteweg-de Vries Equation

2009-04-18

arxiv.org/abs/0904.2819v2

Anal. PDE 2 (2009), no.3, 281-304

Mathematics

Analysis of PDEs

23 pages. Nonlinear analysis is modified

Scientific paper

We prove the local well-posedness of the periodic stochastic Korteweg-de Vries equation with the additive space-time white noise. In order to treat low regularity of the white noise in space, we consider the Cauchy problem in the Besov-type space \hat{b}^s_{p, \infty}(T) for s= -1/2+, p = 2+ such that sp < -1. In establishing the local well-posedness, we use a variant of the Bourgain space adapted to \hat{b}^s_{p, \infty}(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.

Affiliated with

Also associated with

No associations

Rating

Periodic Stochastic Korteweg-de Vries Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Periodic Stochastic Korteweg-de Vries Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Periodic Stochastic Korteweg-de Vries Equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-545861