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

Local representation and construction of Beltrami fields II. Solenoidal Beltrami fields and ideal MHD equilibria