  We analyze the two-field formulation of the quasi-static Biot's equations by
means of the inf-sup theory. For this purpose, we exploit an equivalent
four-field formulation of the equations, introducing the so-called total
pressure and total fluid content as independent variables. We establish
existence, uniqueness and stability of the solution. Our stability estimate is
two-sided and robust, meaning that the regularity established for the solution
matches the regularity requirements for the data and the involved constants are
independent of all material parameters. We prove also that additional
regularity in space of the data implies, in some cases, corresponding
additional regularity in space of the solution. These results are instrumental
to the design and the analysis of discretizations enjoying accurate stability
and error estimates.
