THE PRESSURE EQUATION FOR FLUID-FLOW IN A STOCHASTIC MEDIUM

An equation modelling the pressure p(x) = p(x, omega) at x is an eleme nt of D subset of R(d) of an incompressible fluid in a heterogeneous, isotropic medium with a stochastic permeability k(x,omega) greater tha n or equal to 0 is the stochastic partial differential equation [GRAPH ICS] where f is the given source rate of the fluid, lozenge denotes Wi ck product. We represent k as the positive noise given by the Wick exp onential of white noise, and we find an explicit formula for the (uniq ue) solution p(x, omega), which is proved to belong to the space (S)(- 1) of generalized white noise distributions.