Applicable Analysis ( IF 1.1 ) Pub Date : 2020-04-01 , DOI: 10.1080/00036811.2020.1745779 Weixuan Shi 1, 2 , Jianzhong Zhang 2
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.
中文翻译:
关于可压缩磁流体动力系统时间衰减估计的注记
摘要
本文致力于在恒定平衡(远离真空)附近对可压缩磁流体动力学 (MHD) 方程的全局强解的最佳时间衰减估计 临界 Besov 空间。我们在其中声明了一个新的低频假设,该假设在解决方案的长时间行为中起着关键作用。准确地说,我们证明如果初始数据的低频属于某个 Besov 空间 和 (),那么 标准(略强 范数实际上)的强解具有最优衰减 ( 如果 ) 为了 ,这改进了 [Shi WX, Xu J. 在临界框架中可压缩磁流体动力系统强解的大时间行为。J 双曲线差分方程。2018;15:259–290]。证明主要取决于针对解决方案的低频和高频的尖锐时间加权能量估计。作为副产品,那些最佳时间衰减率—— 类型也被捕获在关键框架中。