ABSTRACT
The present paper is dedicated to the optimal time-decay estimates of global strong solutions near constant equilibrium (away from vacuum) to the compressible magnetohydrodynamic (MHD) equations in the critical Besov spaces. In which we claim a new low-frequency assumption that plays a key role in the large-time behavior of solutions. Precisely, we exhibit that if the low frequencies of initial data belong to some Besov space
with
(
), then the
norm (the slightly stronger
norm in fact) of strong solutions has the optimal decay
(
if
) for
, which improve the results of [Shi WX, Xu J. Large-time behavior of strong solutions to the compressible magnetohydrodynamic system in the critical framework. J Hyperbol Differ Equ. 2018;15:259–290]. The proof mainly depends on a sharp time-weighted energy estimates in light of low and high frequencies for the solutions. As a by-product, those optimal time-decay rates of
-
type are also captured in the critical framework.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 Note that for technical reasons, we need a small overlap between low and high frequencies.