## Multidimensional stochastic Burgers equation

### Zdzisław Brzeźniak, Ben Goldys and Misha Neklyudov

#### Abstract

We consider multidimensional stochastic Burgers equation on the torus $$\mathbb{T}^d$$ and the whole space $$\mathbb{R}^d$$. 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 $$\nu\searrow0$$ for potential solutions. In the case of $$\mathbb{R}^d$$ uniform with respect to $$\nu$$ a priori estimate is established if a Beale-Kato-Majda type condition is satisfied.

Keywords: stochastic Burgers equation, stochastic integral, Beale-Kato-Majda condition, Maximum principle.

: Primary 35K45; secondary 35K55, 35R60, 60H15.

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 Tuesday, October 15, 2013