Lp-Lq-Lr estimates and minimal decay regularity for compressible Euler-Maxwell equations
Lp-Lq-Lr estimates and minimal decay regularity for compressible Euler-Maxwell equations
复制标题
可压缩欧拉-麦克斯韦方程的 Lp-Lq-Lr 估计和最小衰减规律
DOI：
10.1016/j.matpur.2015.07.001
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发表时间：
2015
影响因子：
2.3
通讯作者：
Kawashima Shuichi
中科院分区：
文献类型：
--
作者：
Xu Jiang;Mori Naofumi;Kawashima Shuichi
由于正则性损失的耗散结构，通常施加比全局时间存在时更高的正则性来获得耗散系统经典解的最优衰减率。本文的目的是寻求L 1(Rn)-L 2(Rn)的最优衰减率的最小正则性指数。因此，首次提出了正则性损失耗散系统的最小衰减正则性的概念。为此，我们利用傅立叶空间中的低频和高频分析，得到了L p(Rn)-L q(Rn)-L r(Rn)型的一个新的时间衰变估计。作为应用，对于具有较弱耗散机制的可压缩Euler-Maxwell方程，证明了最小衰减正则性与整体经典解的临界正则性重合。此外，具有非对称耗散的对称双曲组的新近衰减性也被推广到L p-型。
Due to the dissipative structure of regularity-loss, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions to dissipative systems. The aim of this paper is to seek the lowest regularity index for the optimal decay rate of L 1 (R n)–L 2 (R n). Consequently, a notion of minimal decay regularity for dissipative systems of regularity-loss is firstly proposed. To do this, we develop a new time-decay estimate of L p (R n)–L q (R n)–L r (R n) type by using the low-frequency and high-frequency analysis in Fourier spaces. As an application, for compressible Euler–Maxwell equations with the weaker dissipative mechanism, it is shown that the minimal decay regularity coincides with the critical regularity for global classical solutions. Moreover, the recent decay property for symmetric hyperbolic systems with non-symmetric dissipation is also extended to be the L p-version.