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Variational study of interstellar magnetic gas clouds: Theory, modeling, and computation
Herein are described some model problems, means of solution, and some properties of solutions for the equilibrium of self-gravitating isothermal gases in interstellar configurations, with magnetic field. The approach is from the viewpoint of the calculus of variations, with flux-freezing being modelled as well as flux loss through partial ionization. In this work such a treatment is presented for the first time, incorporating aspects of the physical problem as previously studied by authors Woltjer, Mouschovias, and others, and presenting a new application of recently developed variational methods, extending their previous applications from fluid dynamics and terrestrial plasma problems to the present situation. In this approach the problem is formulated and solved as a non-linear, free-boundary problem in variational form with linear and non-linear constraints. The full extent of the matter is considered, from model construction, through construction of solutions to dimensionless PDE, to interpretation of results and their physical and mathematical meaning. Computational methods for calculating the physical and mathematical meaning. Computational methods for calculating the solutions are applied. The construction and justification of this solution method forms the basis for a constructive proof of the existence of solutions. A foundation is prepared for complete analytical investigations of the model or prototype problem, as well as for computational investigation of important realistic physical situations.
Morris, Brian Cleon, "Variational study of interstellar magnetic gas clouds: Theory, modeling, and computation" (1991). Doctoral Dissertations Available from Proquest. AAI9132888.