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We study the generalized Forchheimer flows of slightly compressible fluids inrotating porous media. In the problem's model, the varying density in theCoriolis force is fully accounted for without any simplifications. It resultsin a doubly nonlinear parabolic equation for the density. We derive a prioriestimates for the solutions in terms of the initial, boundary data and physicalparameters, emphasizing on the case of unbounded data. WeightedPoincar\'e-Sobolev inequalities suitable to the equation's nonlinearity,adapted Moser's iteration and maximum principle are used and combined to obtaindifferent types of estimates.

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