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

Authors

EMİNE ÇELİK
LUAN HOANG
THINH KIEU

DOI

10.55730/1300-0098.3405

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 Poincare-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.

Keywords

Forchheimer flows, porous media, compressible fluids, rotating fluids, doubly nonlinear equation, Poincare-Sobolev inequality, Moser iteration, maximum estimates

First Page

949

Last Page

987

Recommended Citation

ÇELİK, EMİNE; HOANG, LUAN; and KIEU, THINH (2023) "Studying a doubly nonlinear model of slightly compressible Forchheimer flows in rotating porous media," Turkish Journal of Mathematics: Vol. 47: No. 3, Article 5. https://doi.org/10.55730/1300-0098.3405
Available at: https://journals.tubitak.gov.tr/math/vol47/iss3/5