Preprint A692/2011
Regularity results for the ordinary product stochastic pressure equation

Marcus Sarkis | Galvis, Juan

**Keywords: **
Stochastic pressure equation | White Noise Analysis | Stochastic Analysis | Weighted Chaos norms | Gaussian Sobolev norms.

We consider a stochastic pressure equation with lognormal coefficient with infinite dimensional noise. Using a White Noise framework, we study spatial and stochastic regularity
of solutions of the stochastic pressure equation. We first establish that a particular class of weighted Chaos spaces
can be characterized by Gaussian Sobolev type norms in the
random argument under the Gaussian measure. Then, we use these results to prove that the solution of the stochastic pressure equation has the classical regularity in the spatial variable and a stochastic regularity on this class of weighted Chaos spaces.