Multidimensional stochastic Burgers equation

Abstract

We consider multidimensional stochastic Burgers equation on the torus ${\mathbb{T}}^d$ and the whole space $\Rd$. In both cases we show that for positive viscosity $\nu >0$ there exists a unique strong global solution in $L^p$ for $p>d$. In the case of torus we also establish a uniform in $\nu$ a priori estimate and consider a limit $ν\todown 0$ for potential solutions. In the case of $\Rd$ uniform with respect to $\nu$ a priori estimate established if a Beale-Kato-Majda type condition is satisfied.

16 pages