The optimal time-decay estimate of solutions to two-fluid Euler-Maxwell equations in the critical Besov space

Limiao Wu; Weixuan Shi; Jiang Xu

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The optimal time-decay estimate of solutions to two-fluid Euler-Maxwell equations in the critical Besov space

机译：临界BESOV空间中的两个流体Euler-Maxwell方程解决方案的最佳时间衰减估计

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摘要

We obtain the optimal time-decay rate of classical solutions to two-fluid Euler- Maxwell equations in ?_N(N = 2, 3), which is a remaining question in the framework of critical Besov space (see [1]). The system is of regularity-loss, so it is difficult to get decay rates in the solution space. In this paper, the new estimate of L_p-L_q-L_r type and something like "square formula of Duhamel principle" are mainly used. It is shown that in the critical Besov space, the solution decays to constant equilibrium at the rate (1 + t)~(-N/2 ( 1/p-1/2 )) with 1 ≤ p < 6∕5 if N = 3 and p = 1 if N = 2.

机译：我们获得了在xn（n = 2,3）中的两个流体euler-maxwell方程的经典解的最佳时间衰减速率，这是关键BESOV空间框架中的剩余问题（参见[1]）。系统具有规则性损失，因此难以在解决方案空间中获得衰减率。在本文中，主要使用了L_P-L_Q-L_R类型的新估计和“Duhamel原理”的“方形公式”。结果表明，在临界BESOV空间中，溶液在速率（1 + T）〜（-N / 2（1/2（1/2（1/2（1/2（1/2））中垂直平衡，如果n为1≤p<6/5 = 3，p = 1如果n = 2。

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来源
《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2019年第11期|共12页
作者
Limiao Wu; Weixuan Shi; Jiang Xu;
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作者单位

Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 211106 P.R. China;

Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 211106 P.R. China;

Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 211106 P.R. China;

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原文格式 PDF
正文语种 eng
中图分类应用数学;力学;
关键词
L_p-L_q -L_r estimates; regularity-loss; minimal decay regularity; two-fluid Euler-Maxwell equations;

机译：L_P-L_Q -L_R估计;规则损失;最小衰减规律性;双流体欧拉 - 麦克斯韦方程;

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专利

1. The optimal time-decay estimate of solutions to two-fluid Euler-Maxwell equations in the critical Besov space [J] . Limiao Wu, Weixuan Shi, Jiang Xu Zeitschrift fur Angewandte Mathematik und Mechanik . 2019,第11期

机译：临界BESOV空间中的两个流体Euler-Maxwell方程解决方案的最佳时间衰减估计
2. Global existence and optimal time-decay estimates of solutions to the generalized double dispersion equation on the framework of Besov spaces [J] . Wang Yuzhu, Xu Jiang, Kawashima Shuichi Journal of Mathematical Analysis and Applications . 2020,第1期

机译：BESOV空间框架上广义双色分散方程解决方案的全局存在和最优时间衰减估计
3. Global Well-Posedness and Time-Decay Estimates of the Compressible Navier-Stokes-Korteweg System in Critical Besov Spaces [J] . Chikami Noboru, Kobayashi Takayuki Journal of mathematical fluid mechanics . 2019,第2期

机译：Passov空间中的可压缩Navier-Stokes-Korteweg系统的全球良好的良好和时间衰减估计
4. Global Solutions of the Euler-Maxwell Two-fluid System in 3D [C] . Yan Guo, Alexandru D. Ionescu, Benoit Pausader International Congress of Chinese Mathematicians . 2016

机译：3D中欧拉麦克斯韦尔两种流体系统的全局解决方案
5. Analysis of the Navier -Stokes and other nonlinear evolution equations with initial data in Besov -type spaces. [D] . Mazzucato, Anna Laura. 2000

机译：用Besov型空间中的初始数据分析Navier-Stokes和其他非线性发展方程。
6. Estimates of bilinear pseudodifferential operators associated to bilinear Hörmander classes in Besov and Triebel–Lizorkin spaces with variable exponents [O] . Jingshi Xu, Jinlai Zhu -1

机译：Besov和Triebel–Lizorkin空间中具有可变指数的与双线性Hörmander类相关的双线性伪微分算子的估计
7. Global well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations [O] . Xu, Jiang, Xiong, Jun, Kawashima, Shuichi 2012

机译：双流体临界Besov空间的全局适定性欧拉 - 麦克斯韦方程组
8. Non-Linear Operations in the Sobolev Spaces H sub p, sup s and the Besov Spaces B sub p, sup s, Q and Regularity for the Semi-Linear Equations [R] . Gramchev, T. V. 1987

机译：sobolev空间中的非线性运算H sub p，sup s和Besov空间B sub p，sup s，Q和半线性方程的正则性

The optimal time-decay estimate of solutions to two-fluid Euler-Maxwell equations in the critical Besov space

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