PreprintMultidimensional stochastic Burgers equationZdzisław Brzeźniak, Ben Goldys and Misha NeklyudovAbstractWe 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 BealeKatoMajda type condition is satisfied. Keywords: stochastic Burgers equation, stochastic integral, BealeKatoMajda condition, Maximum principle.AMS Subject Classification: Primary 35K45; secondary 35K55, 35R60, 60H15.
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