Global Magnetofluidostatic Fields ( an Unsolved Pde Problem )

A satisfactory theory of the Global MagnetoFluidoStatic (GMYS) Fields, where symmetric and non-symmetric configurations can be dealt with on the same footing, has not yet been developed. However the formulation of the Nowhere-Force-Free, Local-Global MFS problem about a given smooth isobaric toroidal surface o (actually, a degenerate initial-value problem) can be weakened so as to include certain generallzed solutions as formal power series in a "natural" transverse coordinate. lt is reasonable to conjecture that these series converge, for sufficiently smooth data on . in the same function space which their coefficients belong to (in esO’ sence, a complete linear space over the 2-torus).