  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.
