Structural conditions for full MHD equations
Author:
Bongsuk Kwon
Journal:
Quart. Appl. Math. 67 (2009), 593-600
MSC (2000):
Primary 35B35
DOI:
https://doi.org/10.1090/S0033-569X-09-01139-6
Published electronically:
May 14, 2009
MathSciNet review:
2547642
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this paper, we investigate the characteristic structure of the full equations of magnetohydrodynamics (MHD) and show that it satisfies the hypotheses of a general variable-multiplicity stability framework introduced by Métivier and Zumbrun, thereby extending to the general case various results obtained by Métivier and Zumbrun for the isentropic equations of MHD.
References
- A. M. Blokhin, Strong discontinuities in magnetohydrodynamics, Nova Science Publishers, Inc., Commack, NY, 1994. Translated by A. V. Zakharov. MR 1406089
- Alexander Blokhin and Yuri Trakhinin, Stability of strong discontinuities in fluids and MHD, Handbook of mathematical fluid dynamics, Vol. I, North-Holland, Amsterdam, 2002, pp. 545–652. MR 1942469, DOI https://doi.org/10.1016/S1874-5792%2802%2980013-1
- A. M. Blokhin and Yu. L. Trakhinin, Stability of fast parallel MHD shock waves in polytropic gas, Eur. J. Mech. B Fluids 18 (1999), no. 2, 197–211. MR 1681896, DOI https://doi.org/10.1016/S0997-7546%2899%2980022-3
- Jerome J. Erpenbeck, Stability of step shocks, Phys. Fluids 5 (1962), 1181–1187. MR 155515, DOI https://doi.org/10.1063/1.1706503
- Andrew Majda, The stability of multidimensional shock fronts, Mem. Amer. Math. Soc. 41 (1983), no. 275, iv+95. MR 683422, DOI https://doi.org/10.1090/memo/0275
- Guy Métivier and Kevin Zumbrun, Hyperbolic boundary value problems for symmetric systems with variable multiplicities, J. Differential Equations 211 (2005), no. 1, 61–134. MR 2121110, DOI https://doi.org/10.1016/j.jde.2004.06.002
References
- A.M. Blokhin, Strong Discontinuities in Magnetohydrodynamics. Translated by A. V. Zakharov. Nova Science Publishers, Inc., Commack, NY, 1994. x+150 pp. ISBN: 1-56072-144-8. MR 1406089 (97c:76069)
- A. Blokhin and Y. Trakhinin, Stability of strong discontinuities in fluids and MHD. In Handbook of Mathematical Fluid Dynamics, Vol. I, 545–652, North-Holland, Amsterdam, 2002. MR 1942469 (2004i:76117)
- A.M. Blokhin and Y. Trakhinin, Stability of fast parallel MHD shock waves in polytropic gas. Eur. J. Mech. B Fluids 18 (1999) 197–211. MR 1681896 (99m:76117)
- J.J. Erpenbeck, Stability of step shocks, Phys. Fluids 5 (10) (1962) 1181-1187. MR 0155515 (27:5449)
- A. Majda, The stability of multi-dimensional shock fronts. Mem. Amer. Math. Soc. 41, no. 275 (1983) iv+95 pp. MR 683422 (84e:35100)
- G. Metivier, K. Zumbrun, Hyperbolic boundary value problems for symmetric systems with variable multiplicities, J. Differential Equations 211 (2005) 61-134. MR 2121110 (2005j:35145)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2000):
35B35
Retrieve articles in all journals
with MSC (2000):
35B35
Additional Information
Bongsuk Kwon
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Address at time of publication:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email:
bkwon@indiana.edu
Received by editor(s):
July 3, 2008
Published electronically:
May 14, 2009
Additional Notes:
The author thanks Kevin Zumbrun for suggesting the problem. This work was partially supported under NSF grant DMS-0300487
Article copyright:
© Copyright 2009
Brown University
