White Noise Driven Korteweg–de Vries Equation

Periodic Solutions of the Korteweg-de Vries Equation Driven by White Noise

Abstract. We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time and “almost white in space”. We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the metho...

On Stochastic Navier-Stokes Equation Driven by Stationary White Noise

We consider an unbiased approximation of stochastic Navier-Stokes equation driven by spatial white noise. This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The nonlinear term can be characterized as the highest stochastic order approximation of the original nonlinear term u∇u. We investigate the analyti...

The Stochastic Transport Equation Driven by Lévy White Noise

In this paper we demonstrate how concepts of white noise analysis can be used to give an explicit solution to a stochastic transport equation driven by Lévy white noise.

The Korteweg-de Vries Equation with Multiplicative Homogeneous Noise

We prove the global existence and uniqueness of solutions both in the energy space and in the space of square integrable functions for a Korteweg-de Vries equation with noise. The noise is multiplicative, white in time, and is the muliplication by the solution of a homogeneous noise in the space variable.

Stochastic heat equation with white-noise drift