Multidimensional Stochastic Burgers Equation

Multidimensional Stochastic Burgers Equation

We consider multidimensional stochastic Burgers equation on the torus T and the whole space R . In both cases we show that for positive viscosity ν > 0 there exists a unique strong global solution in L for p > d. In the case of torus we also establish a uniform in ν a priori estimate and consider a limit ν ↘ 0 for potential solutions. In the case of R uniform with respect to ν a priori estimate...

Algorithm refinement for the stochastic Burgers' equation

In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers’ equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus ...

Large Deviations for a Stochastic Burgers’ Equation

We prove the large deviations principle (LDP) for the law of the solutions to a stochastic Burgers’ equation in the presence of an additive noise. Our proof is based on the weak convergence approach.

On Numerical Approximation of Stochastic Burgers’ Equation

Approximations to the Stochastic Burgers Equation

This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in space and in time. We demonstrate that in this case, different finite difference schemes converge to different limiting processes as the mesh size tends to zero....