Plane one-dimensional MHD flows: Symmetries and conservation laws

  title={Plane one-dimensional MHD flows: Symmetries and conservation laws},
  author={V. A. Dorodnitsyn and E. I. Kaptsov and Roman Kozlov and Sergey V. Meleshko and Potcharapol Mukdasanit},
  journal={International Journal of Non-Linear Mechanics},
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and conservation laws. For the case of the finite electric conductivity we establish Lie group classification, i.e. we describe all cases of the conductivity σ(ρ, p) for which there are symmetry extensions. The conservation laws are derived by the direct computation… 
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