MULTIDIMENSIONAL STOCHASTIC BURGERS EQUATION

作者：Brzezniak Zdzislaw^*; Goldys Ben; Neklyudov Misha

来源：SIAM Journal on Mathematical Analysis, 2014, 46(1): 871-889.

DOI：10.1137/120866117

• stochastic Burgers equation
• Beale-Kato-Majda condition
• vanishing viscosity

We consider multidimensional stochastic Burgers equation on the torus T-d and the whole space R-d. In both cases we show that for positive viscosity nu %26gt; 0 there exists a unique strong global solution in L-p for p %26gt; d. In the case of the torus we also establish a uniform in nu a priori estimate and consider a limit nu SE arrow 0 for potential solutions. In the case of R-d uniform with respect to nu a priori estimate established if a Beale-Kato-Majda-type condition is satisfied.

• 出版日期2014