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Weak and Strong Solutions of Equations of Compressible Magnetohydrodynamics

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Xavier Blanc

    (Laboratoire Jacques-Louis Lions, Univ. Paris Diderot, Sorbonne Paris Cité)

  • Bernard Ducomet

    (CEA/DAM Ile De France, Département de Physique Théorique et Appliquée)

Abstract

This article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling assumptions. Then, we report on the results of existence of weak solutions, using the notion of renormalized solutions. Next, existence of strong solutions in the neighborhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted: the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques.

Suggested Citation

  • Xavier Blanc & Bernard Ducomet, 2018. "Weak and Strong Solutions of Equations of Compressible Magnetohydrodynamics," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 51, pages 2869-2925, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_72
    DOI: 10.1007/978-3-319-13344-7_72
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