Global estimates for generalized Forchheimer flows of slightly compressible fluids

Luan Hoang, Thinh Kieu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
JournalJournal d'Analyse Mathematique
Volume137
Issue number1
DOIs
StatePublished - Mar 1 2019

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