  We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A
study of continuity properties of the Bogovskii -operator between Orlicz spaces
is a crucial step, of independent interest, in our approach. Applications to
the problem of pressure reconstruction for Non-Newtonian fluids governed by
constitutive laws, which are not necessarily power type, are presented. A key
inequality for a numerical analysis of the underlying elliptic system is also
derived.
