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Journal d'Analyse Mathématique

, Volume 137, Issue 1, pp 1–55 | Cite as

Global estimates for generalized Forchheimer flows of slightly compressible fluids

  • Luan HoangEmail author
  • Thinh Kieu
Article
  • 19 Downloads

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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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.Department Of MathematicsUniversity Of North Georgia, Gainesville CampusOakwoodUSA

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