  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 $\nu\todown 0$ 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.
