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We investigate the Cauchy problem to the compressible planar non-resistivemagnetohydrodynamic equations with zero heat conduction. The global existenceof strong solutions to such a model has been established by Li and Li (J.Differential Equations 316: 136--157, 2022). However, to our best knowledge, sofar there is no result on the behavior of the entropy near the vacuum regionfor this model. The main novelty of this paper is to give a positive responseto this problem. More precisely, by a series of a priori estimates, especiallythe singular type estimates, we show that the boundedness of the entropy can bepropagated up to any finite time provided that the initial vacuum presents onlyat far fields with sufficiently slow decay of the initial density.

Entropy-bounded solutions to the Cauchy problem of compressible planar non-resistive magnetohydrodynamics equations with far field vacuum