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Global estimates for generalized Forchheimer flows of slightly compressible fluids

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Abstract

This paper is focused on the generalized Forchheimer flows of slightly compressible fluids in porous media. They are reformulated as a degenerate parabolic equation for the pressure. The initial boundary value problem is studied with time-dependent Dirichlet boundary data. The estimates up to the boundary and for all time are derived for the L∞-norm of the pressure, its gradient and time derivative. Large-time estimates are established to be independent of the initial data. Particularly, thanks to the special structure of the pressure’s nonlinear equation, the global gradient estimates are obtained in a relatively simple way, avoiding complicated calculations and a prior requirement of Hölder estimates.

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Author information

Authors and Affiliations

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

    Luan Hoang

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

    Thinh Kieu

Authors
  1. Luan Hoang
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  2. Thinh Kieu
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Corresponding author

Correspondence to Luan Hoang.

Additional information

Dedicated to Professor Duong Minh Duc with gratitude

Supported by NSF grant DMS-1412796

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Hoang, L., Kieu, T. Global estimates for generalized Forchheimer flows of slightly compressible fluids. JAMA 137, 1–55 (2019). https://doi.org/10.1007/s11854-018-0064-5

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  • DOI: https://doi.org/10.1007/s11854-018-0064-5

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