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Generalized Forchheimer Flows of Isentropic Gases

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Abstract

We consider generalized Forchheimer flows of either isentropic gases or slightly compressible fluids in porous media. By using Muskat’s and Ward’s general form of the Forchheimer equations, we describe the fluid dynamics by a doubly nonlinear parabolic equation for the appropriately defined pseudo-pressure. The volumetric flux boundary condition is converted to a time-dependent Robin-type boundary condition for this pseudo-pressure. We study the corresponding initial boundary value problem, and estimate the \(L^\infty \) and \(W^{1,2-a}\) (with \(0<a<1\)) norms for the solution on the entire domain in terms of the initial and boundary data. It is carried out by using a suitable trace theorem and an appropriate modification of Moser’s iteration.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Nevada, Reno, NV , 89557, USA

    Emine Celik

  2. Department of Mathematics and Statistics, Texas Tech University, Box 41042 , Lubbock, TX , 79409-1042, USA

    Luan Hoang

  3. Department of Mathematics, University of North Georgia, Gainesville Campus, 3820 Mundy Mill Rd., Oakwood, GA , 30566, USA

    Thinh Kieu

Authors
  1. Emine Celik
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  2. Luan Hoang
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  3. Thinh Kieu
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Correspondence to Luan Hoang.

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Communicated by E. Feireisl

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Celik, E., Hoang, L. & Kieu, T. Generalized Forchheimer Flows of Isentropic Gases. J. Math. Fluid Mech. 20, 83–115 (2018). https://doi.org/10.1007/s00021-016-0313-2

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