Global magnetofluidostatic fields (an unsolved PDE problem)

Abstract

A satisfactory theory of the Global MagnetoFluidoStatic (GMFS) 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 surface𝒮0(actually, a degenerate initial-value problem) can be weakened so as to include certain generalized solutions as formal power series in a “natural” transverse coordinate. lt is reasonable to conjecture that these series converge, for sufficiently smooth data on𝒮0. in the same function space which their coefficients belong to (in essence, a complete linear space over the2-torus).