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

TL;DR

This paper investigates a complex nonlinear model of fluid flow in rotating porous media, accounting for density variations and deriving estimates using advanced mathematical techniques, contributing to understanding such flows in geophysical contexts.

Contribution

It introduces a doubly nonlinear parabolic equation model for compressible Forchheimer flows in rotating media, with new a priori estimates and analytical methods for unbounded data.

Findings

Derived a priori estimates for the nonlinear flow model.

Developed weighted inequalities tailored to the equation's nonlinearity.

Applied advanced mathematical techniques to analyze the model's solutions.

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 Poincar\'e-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.