Multidimensional stochastic Burgers equation

Details Multidimensional stochastic Burgers equation Multidimensional stochastic Burgers equation

2012-02-15

arxiv.org/abs/1202.3230v1

Physics

Mathematical Physics

16 pages

Scientific paper

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.

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