  It is shown that large classes of nonlinear systems of PDEs, with possibly
associated initial and/or boundary value problems, can be solved by the method
of order completion. The solutions obtained can be assimilated with Hausdorff
continuous functions. The usual Navier-Stokes equations, as well as their
various modifications aiming at a realistic modelling are included as
particular cases. The same holds for the critically important constitutive
relations in various branches of Continuum Mechanics. The solution method does
not involve functional analysis, nor various Sobolev or other spaces of
distributions or generalized functions. The general and type independent
existence and regularity results regarding solutions presented here are a first
in the literature.
