  Object of the present paper is the local theory of solution for steady ideal
Euler flows and ideal MHD equilibria. The present analysis relies on the
Lie-Darboux theorem of differential geometry and the local theory of
representation and construction of Beltrami fields developed in [1]. A theorem
for the construction of harmonic orthogonal coordinates is proved. Using such
coordinates families of solenoidal Beltrami fields with different topologies
are obtained in analytic form. Existence of global solenoidal Beltrami fields
satisfying prescribed boundary conditions while preserving the local
representation is considered. It is shown that only singular solutions are
admissible, an explicit example is given in a spherical domain, and a theorem
on existence of singular solutions is proven. Local conditions for existence of
solutions, and local representation theorems are derived for generalized
Beltrami fields, ideal MHD equilibria, and general steady ideal Euler flows.
The theory is applied to construct analytic examples.
