Studying a doubly nonlinear model of slightly compressible Forchheimer flows in rotating porous media

Emine Çelik, Luan Hoang, Thinh Kieu

Research output: Contribution to journalArticlepeer-review

Abstract

We study the generalized Forchheimer flows of slightly compressible fluids in rotating porous media. In the problem’s model, the varying density in the Coriolis force is fully accounted for without any simplifications. It results in a doubly nonlinear parabolic equation for the density. We derive a priori estimates for the solutions in terms of the initial, boundary data and physical parameters, emphasizing on the case of unbounded data. Weighted Poincaré– Sobolev inequalities suitable to the equation’s nonlinearity, adapted Moser’s iteration, and maximum principle are used and combined to obtain different types of estimates.

Original languageEnglish
Pages (from-to)949-987
Number of pages39
JournalTurkish Journal of Mathematics
Volume47
Issue number3
DOIs
StatePublished - 2023

Keywords

  • Forchheimer flows
  • Moser iteration
  • Poincaré– Sobolev inequality
  • compressible fluids
  • doubly nonlinear equation
  • maximum estimates
  • porous media
  • rotating fluids

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