Abstract
The property of fluid field of one-dimensional magnetohydrodynamics (MHD) transverse flow after the appearance of singularity is discussed. By the method of iteration, the strong discontinuity (shock wave) and entropy solution are constructed and the estimations on the singularity of the solution near the point of blow up are obtained.
Similar content being viewed by others
References
Sideris T C. Formation of singularities in three dimensional compressible fluid [J].Comm Math Phys, 1985,101(3):475–485.
Rammaha M A. On the formation of singularities in magneto-hynanic waves[J].J Math Anal Appl, 1994,188(3):940–955.
KONG De-xing. Cauchy problem for quasilinear hyperbolic systems[D]. Thesis for PhD Degree. Shanghai: Fudan University, 1993. (in Chinese)
DONG Li-ming. Formation of shock waves by quasilinear hyperbolic equations[D]. Thesis for PhD Degree. Shanghai: Fudan University, 1999. (in Chinese)
Lebaud M P. Description de ca formation d'un choc dans le p-systems [J].J Math Pure Appl, 1994,73(6):523–565.
Author information
Authors and Affiliations
Additional information
Communicated by Dai Shi-qiang
Biographies: Dong Li-ming (1972-), Doctor; Shi Yi-peng (1972-), Doctor
Rights and permissions
About this article
Cite this article
Li-ming, D., Yi-peng, S. The formation of shock waves of the equations of magnetohydrodynamics. Appl Math Mech 22, 1064–1073 (2001). https://doi.org/10.1007/BF02438325
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02438325