## Abstract

An equation modelling the pressure*p*(*x*) =*p*(*x, w*) at*x* ∈*D* ⊂**R**
^{d} of an incompressible fluid in a heterogeneous, isotropic medium with a stochastic permeability*k*(*x, w*) ≥ 0 is the stochastic partial differential equation

where*f* is the given source rate of the fluid, ◊ denotes Wick product.

We represent*k* as the positive noise given by the Wick exponential of white noise, and we find an explicit formula for the (unique) solution*p*(*x, w*), which is proved to belong to the space (*S*)^{−1} of generalized white noise distributions.

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Holden, H., Lindstrøm, T., Øksendal, B. *et al.* The pressure equation for fluid flow in a stochastic medium.
*Potential Anal* **4**, 655–674 (1995). https://doi.org/10.1007/BF02345830

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DOI: https://doi.org/10.1007/BF02345830