Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

Luan T. Hoang, Thinh T. Kieu

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Abstract

The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time, the interior L (L ∞} -estimates for the pressure, its gradient and time derivative, and the interior L 2 L 2 -estimates for its Hessian. The De Giorgi and Ladyzhenskaya-Uraltseva iteration techniques are used taking into account the special structures of the equations for both pressure and its gradient. These are combined with the uniform Gronwall-type bounds in establishing the asymptotic estimates when time tends to infinity.

Original languageEnglish
Pages (from-to)739-767
Number of pages29
JournalAdvanced Nonlinear Studies
Volume17
Issue number4
DOIs
StatePublished - Oct 1 2017

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Keywords

  • Asymptotic
  • Darcy-Forchheimer Equation
  • Degenerate Parabolic Equation
  • Nonlinear Differential Inequality
  • Porous Media
  • Stability
  • Uniform Gronwall Inequality

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