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Stochastic elliptic–parabolic system arising in porous media

Hakima Bessaih

https://orcid.org/0000-0002-2231-5586

Mathematics & Statistics, Florida International University, 11200 S.W. 8^th St., Miami, FL 33199, USA

E-mail Address: hbessaih@fiu.edu

Corresponding author.

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Cynthia Cohn

Mathematics & Statistics, University of Wyoming, University Ave., Laramie, WY 82071, USA

E-mail Address: ccohn@uwyo.edu

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Oussama Landoulsi

Mathematics & Statistics, Florida International University, 11200 S.W. 8^th St., Miami, FL 33199, USA

E-mail Address: olandoul@fiu.edu

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https://doi.org/10.1142/S0219493722400226Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue in Memory of María J. Garrido-Atienza
Guest Editor: Tomas Caraballo

Abstract

We prove the existence of a pathwise weak solution to the single-phase, miscible displacement of one incompressible fluid by another in a porous medium with random forcing. Our system is described by a parabolic concentration equation driven by an additive noise coupled with an elliptic pressure equation. We use a pathwise argument combined with Schauder’s fixed point theorem.

Keywords:

AMSC: 76S05, 35K60, 60H15, 60H25, 60G05

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