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

2021/06/22 by Emine Çelik, Celik, Emine, Luan Hoang +3 · 3 citations
Chemical Engineering · Computer Science · Engineering · #35K20 #35K65 #76S05 #76U60 #86A05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.2106.11925

openalex publication_date 2021/06/22 · openalex created_date 2023/03/26 · openalex updated_date 2026/07/28

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.

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• On compressible fluid flows of Forchheimer-type in rotating heterogeneous porous media
• Asymptotic estimates for solutions of inhomogeneous non-divergence diffusion equations with drifts
• A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media

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