The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system
The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system
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DOI：
10.1142/s0219891616500193
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发表时间：
2016-12
影响因子：
0.7
通讯作者：
Jiang Xu;S. Kawashima
中科院分区：
文献类型：
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作者：
Jiang Xu;S. Kawashima
可压缩欧拉-麦克斯韦双流体系统是磁化等离子体数值模拟中的一个重要问题。我们首先设计了关键的能量泛函来捕捉它的耗散结构，由于电子和离子之间的非线性耦合和抵消，整个空间ℝ3的耗散结构相对于单流体情况相对较弱。此外，借助于Lp(ℝn)-Lq(ℝn)-LR(ℝn)时间衰减估计，我们得到了光滑解全局时间存在的临界正则性(sc=3)的L1(ℝ3)-L2(ℝ3)衰减率，解决了[Y.J.Peng，双流体EulerMaxwell方程光滑解的全局存在性和长时间性态]一文[Y.J.Peng，Global Experience and Long-time Behavior of Two-Fluid EulerMaxwell方程，AN.IHP肛门。非线报29(2012)737-759]。
The compressible Euler–Maxwell two-fluid system arises in the modeling of magnetized plasmas. We first design crucial energy functionals to capture its dissipative structure, which is relatively weaker in comparison with the one-fluid case in the whole space ℝ3, due to the nonlinear coupling and cancelation between electrons and ions. Furthermore, with the aid of Lp(ℝn)-Lq(ℝn)-Lr(ℝn) time-decay estimates, we obtain the L1(ℝ3)-L2(ℝ3) decay rate with the critical regularity (sc = 3) for the global-in-time existence of smooth solutions, which solves the decay problem left open in [Y. J. Peng, Global existence and long-time behavior of smooth solutions of two-fluid Euler–Maxwell equations, Ann. IHP Anal. Non Lineaire 29 (2012) 737–759].