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Various formulations and approximations of incompressible fluid motions in porous media

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Abstract

We first recall various formulations and approximations for the motion of an incompressible fluid, in the well-known setting of the Euler equations. Then, we address incompressible motions in porous media, through the Muskat system, which is a friction dominated first order analog of the Euler equations for inhomogeneous incompressible fluids subject to an external potential.

Résumé

On commence par rappeler plusieurs formulations et approximations décrivant le mouvement d’un fluide incompressible dans le cadre bien connu des équations d’Euler. On s’intéresse ensuite aux mouvements incompressibles en milieux poreux, au travers du système de Muskat, qui est un analogue du premier ordre, dominé par la friction, des équations d’Euler pour des fluides incompressibles inhomogènes soumis à un potentiel extérieur.

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  1. CNRS, DMA-ENS, 45 rue d’Ulm, 75005, Paris, France

    Yann Brenier

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Brenier, Y. Various formulations and approximations of incompressible fluid motions in porous media. Ann. Math. Québec 46, 195–206 (2022). https://doi.org/10.1007/s40316-021-00178-2

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