Authors: EMİNE ÇELİK, LUAN HOANG, THINH KIEU

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

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