Previous |  Up |  Next


magnetohydrodynamics; radiation transport; local existence
We consider a system of balance laws describing the motion of an ionized compressible fluid interacting with magnetic fields and radiation effects. The local-in-time existence of a unique smooth solution for the Cauchy problem is proven. The proof follows from the method of successive approximations.
[1] H. Cabannes: Theoretical Magnetofluiddynamics. Academic Press, New York-London, 1970.
[2] A. Dedner, C. Rohde: A scalar model problem in radiation hydrodynamics. In preparation.
[3] K. O. Friedrichs: On the laws of relativistic electromagnetofluid dynamics. Comm. Pure Appl. Math. 27 (1974), 749–808. MR 0375928
[4] K. O. Friedrichs: Conservation equations and the laws of motion in classical physics. Comm. Pure Appl. Math. 32 (1978), 123–131. MR 0509916 | Zbl 0379.35002
[5] K. Hamer: Nonlinear effects on the propagation of sound waves in a radiating gas. Quart. J.  Mech. Appl. Math. 24 (1971), .
[6] K. Ito: BV-solutions of the hyperbolic-elliptic system for a radiating gas. Preprint (1999).
[7] T. Kato: The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rational Mech. Anal. 58 (1975), 181–205. DOI 10.1007/BF00280740 | MR 0390516 | Zbl 0343.35056
[8] S. Kawashima, Y. Nikkuni and S. Nishibata: The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics. In: Analysis of systems of conservation laws, H. Freistühler (ed.), Chapman&Hall monographs and surveys in pure and applied mathematics 99, 1998, pp. 87–127. MR 1679939
[9] A. Majda: Compressible Fluid Flow and Systems of Conservations Laws in Several Space Variables. Springer, 1984. MR 0748308
[10] D. Mihalas: Radiation hydrodynamics. In: Computational methods for astrophysical fluid flow. Saas-Fee advanced course 27.  Lecture notes  1997, O. Steiner et al. (eds.), Swiss Society for Astrophysics and Astronomy, 1998, pp. 161–261. Zbl 0940.76083
[11] W. G. Vincenti, C. H. Krueger: Introduction to Physical Gas Dynamics. Wiley, 1965.
[12] W. Zajączkowski: Non-characteristic mixed problems for nonlinear symmetric hyperbolic systems. Math. Methods Appl. Sci. 11 (1989), 139–168. DOI 10.1002/mma.1670110201
Partner of
EuDML logo