L∞ continuation principle to the non‐baratropic non‐resistive magnetohydrodynamic equations without heat conductivity

The aim of this paper is to establish a continuation principle for strong solutions to the full compressible magnetohydrodynamic system without resistivity and heat conductivity. We prove that if the solution loses its regularity in finite time, the dominated part is due to the hyperbolic effect. More precisely, it is essentially shown that the strong solution exists globally if the density, temperature, and magnetic field are bounded from above, where vacuum is allowed to exist. This verifies a problem proposed by D.Serre. Copyright © 2016 John Wiley & Sons, Ltd.