One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws

A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in mass Lagrangian coordinates. This analyses with cylindrical symmetry The medium is assumed inviscid thermally non-conducting. It modeled by a polytropic gas. Symmetries are found. cases finite infinite electric conductivity need to be analyzed separately. For $\sigma (\rho,p)$ we perform Lie group classification, which identifies additional symmetries. found direct computation. variational formulations equations considered. classifications obtained entropy treated as an arbitrary element. formulation allows use Noether theorem computation laws. also presented original (physical) variables.