| Title:
|
On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation (English) |
| Author:
|
Rohde, C. |
| Author:
|
Zajączkowski, W. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
257-277 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
magnetohydrodynamics |
| Keyword:
|
radiation transport |
| Keyword:
|
local existence |
| MSC:
|
35L60 |
| MSC:
|
35Q35 |
| MSC:
|
76N10 |
| MSC:
|
76W05 |
| idZBL:
|
Zbl 1099.35060 |
| idMR:
|
MR1994377 |
| DOI:
|
10.1023/A:1026010631074 |
| . |
| Date available:
|
2009-09-22T18:13:59Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134532 |
| . |
| Reference:
|
[1] H. Cabannes: Theoretical Magnetofluiddynamics.Academic Press, New York-London, 1970. |
| Reference:
|
[2] A. Dedner, C. Rohde: A scalar model problem in radiation hydrodynamics.In preparation. |
| Reference:
|
[3] K. O. Friedrichs: On the laws of relativistic electromagnetofluid dynamics.Comm. Pure Appl. Math. 27 (1974), 749–808. MR 0375928 |
| Reference:
|
[4] K. O. Friedrichs: Conservation equations and the laws of motion in classical physics.Comm. Pure Appl. Math. 32 (1978), 123–131. Zbl 0379.35002, MR 0509916 |
| Reference:
|
[5] K. Hamer: Nonlinear effects on the propagation of sound waves in a radiating gas.Quart. J. Mech. Appl. Math. 24 (1971), . |
| Reference:
|
[6] K. Ito: BV-solutions of the hyperbolic-elliptic system for a radiating gas.Preprint (1999). |
| Reference:
|
[7] T. Kato: The Cauchy problem for quasi-linear symmetric hyperbolic systems.Arch. Rational Mech. Anal. 58 (1975), 181–205. Zbl 0343.35056, MR 0390516, 10.1007/BF00280740 |
| Reference:
|
[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 |
| Reference:
|
[9] A. Majda: Compressible Fluid Flow and Systems of Conservations Laws in Several Space Variables.Springer, 1984. MR 0748308 |
| Reference:
|
[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 |
| Reference:
|
[11] W. G. Vincenti, C. H. Krueger: Introduction to Physical Gas Dynamics.Wiley, 1965. |
| Reference:
|
[12] W. Zajączkowski: Non-characteristic mixed problems for nonlinear symmetric hyperbolic systems.Math. Methods Appl. Sci. 11 (1989), 139–168. 10.1002/mma.1670110201 |
| . |
