International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 123-130
doi:10.1155/S0161171286000157
Global magnetofluidostatic fields (an unsolved PDE problem)
Associazione EURATOM–ENEA sulla Fusione, Centro Ricerche Energia Frascati, C.P. 65 - 00044 Frascati, Roma, Italy
Received 12 October 1984
Copyright © 1986 C. Lo Surdo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 surface 𝒮0 (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 on 𝒮0. in the same function space which their coefficients belong to (in essence, a complete linear space over the 2-torus).