  We consider a class of viscous fluids with a general monotone dependence of
the viscous stress on the symmetric velocity gradient. We introduce the concept
of dissipative solution to the associated initial boundary value problem
inspired by the measure-valued solutions for the inviscid (Euler) system. We
show the existence as well as the weak-strong uniqueness property in the class
of dissipative solutions. Finally, the dissipative solution enjoying certain
extra regularity coincides with a strong solution of the same problem.
