Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

Luan T. Hoang; Thinh T. Kieu

doi:10.1515/ans-2016-6027

Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

Luan T. Hoang, Thinh T. Kieu

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English
Pages (from-to)	739-767
Number of pages	29
Journal	Advanced Nonlinear Studies
Volume	17
Issue number	4
DOIs	https://doi.org/10.1515/ans-2016-6027
State	Published - Oct 1 2017

Keywords

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

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