  In the study of local regularity of weak solutions to systems related to
incompressible viscous fluids local energy estimates serve as important
ingredients. However, this requires certain informations on the pressure. This
fact has been used by V. Scheffer in the notion of a suitable weak to the
Navier-Stokes equation, and in the proof of the partial regularity due to
Caffarelli. Kohn and Nirenberg. In general domains, or in case of complex
viscous fluid models a global pressure doesn't necessarily exist. To overcome
this problem, in the present paper we construct a local pressure distribution
by showing that every distribution $ \partial _t \bu +\bF $, which vanishs on
the set of smooth solenoidal vector fields can be represented by a distribution
$ \partial _t \nabla p_h +\nabla p_0 $, where $\nabla p_h \sim \bu $ and $
\nabla p_0 \sim \bF$.
