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The work presented in this report originated in connection with a research project in magneto-hydrodynamics conducted by Professor H. Grad at the Institute of Mathematical Sciences at New York Univer sity; the report was completed while the author was a consultant at Los Alamos Scientific Laboratory. The report contains an expository analysis of the mathematical structure of magneto-hydrodynamic theory; specifically, of the theory of the interaction of magnetic fields with conducting compressible fluids. One of the major aims is to emphasize the remarkably close parallelism between this theory and ordinary gas dynamics. While hydromagnetic shocks and small disturbance waves have been treated before, it seems that hydromagnetic 'simple waves" are here treated for the first time. In a typical example it is shown that - as in gas dynamics - simple one-dimensional flow problems can be solved with the aid of shocks and simple waves. Throughout the exposition a familiarity with the basic notions of gas dynamics - covered e.g. by the first three chapters of Super sonic ~low and Shock Waves - is presupposed. The bibliography refers only to those papers which are concerned with the subjects treated. No reference is made to a number of sig nificant contributions to hydromagnetics concerned with subjects - such as astro- and geophysical applications, effect of turbulence, stabil ity questions - which are not covered in this report.
List of contents
- Volume 2.- II Papers in Spectral Theory Commentaries by Tosio Kato.- [34-1] Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren.- [34-2] Beiträge zur Theorie der Spektralschar.- [35-1] Über die ausgezeichnete Randbedingung in der Spektraltheorie der halbbeschränkten gewöhnlichen Differentialoperatoren zweiter Ordnung.- [38-1] Über die Spektralzerlegung eines Integraloperators.- [48-1] Criteria for the discrete character of the spectra of ordinary differential operators.- [48-8] On the perturbation of continuous spectra.- [66-2] Spectral Perturbation Phenomena.- III Papers in Elasticity Commentaries by Fritz John.- [41-2] The non-linear boundary value problem of the buckled plate (With, J.J. Stoker).- [42-2] Buckling of the circular plate beyond the critical thrust, (With, J.J. Stoker).- [47-2] On the boundary-value problems of the theory of elasticity and Korn's inequality.- IV Papers in Asymptotics.- [46-1] Singular perturbations of non-linear oscillations, (With W. Wasow).- [55-2] Asymptotic phenomena in mathematical physics (Gibbs Lecture of American Mathematical Society).- V Contributions to Magnetohydrodynamics Harold Weitzner.- [54-1] Nonlinear wave motion in magneto-hydrodynamics.- [78-1] Conservation equations and the laws of motion in classical physics.- VI Papers involving Variational Problems Commentaries by Louis Nirenberg.- [29-4] Ein Verfahren der Variationsrechnung, das Minimum eines Integrals als das Maximum eines anderen Ausdruckes darzustellen.- [33-1] Über ein Minimumproblem für Potentialströmungen mit freiem Rande.- VII Other Papers.- [37-1] On certain inequalities and characteristic value problems for analytic functions and for functions of two variables.- [54-2] The existenceof solitary waves, (With D.H. Hyers).- [55-1] Differential forms on Riemannian manifolds.- [27-1] Eine invariante Formulierung des Newtonschen Gravitationsgesetzes und des Grenzuberganges vom Einsteinschen zum Newtonschen Gesetz.- [80-1] Von Neumann's Hilbert space theory and partial differential equations, (Von Neumann Lecture to Society for Industrial and Applied Mathematics).- [81-1] Unobserved observables and unobserved causality.- VIII Contributions to Quantum Mechanics by David Isaacson.- Honorary Doctoral Degrees.- Awards.- Acknowledgements.
