“…where C T k = C k are symmetric matrices and v k being the velocity field. The latter analysis by Godunov and Romenski in nineties in a series of papers [32,43,30,42,42,87,21,41] of various equations (ideal MHD equations, nonlinear elasticity, electrodynamics of slowly moving medium, superfluid flow, superconductivity) studied in the books of Landau and Lifshitz [62,61] reveals that for a proper understanding of the structure of the continuum mechanics models it is important to distinguish the Lagrangian and Eulerian frames of reference, and that the original Godunov structure (4) is, in fact, rather inherent to the conservation laws written in the Lagrangian frame, while their Eulerian counterparts are inherently non-conservative time evolutions and have more complicated structure (10).…”