= Ideal magnetohydrodynamic equations
{title2=$\partial_t\mathbf U+A_i(\mathbf U)\partial_i\mathbf U=0$}
The smooth ideal-MHD system couples <mass conservation>, <momentum>, adiabatic <pressure> transport and the <ideal magnetohydrodynamic induction equation>, subject to the <solenoidal magnetic-field constraint>. Without gravity it is a <quasilinear partial differential equation> system. Across shocks, conservative total energy replaces smooth adiabatic <pressure> transport.
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