带非线性阻尼项的三维可压缩欧拉方程组的整体解

数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1111-1122.

带非线性阻尼项的三维可压缩欧拉方程组的整体解

朱旭生¹|李芳娥^1,2

1.华东交通大学基础科学学院南昌 330013|2.新乡第一中学河南新乡 453000

收稿日期:2013-04-08 修回日期:2014-03-17 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
国家自然科学基金(11161021, 61262031)和江西省高校科技落地计划项目(KJLD12067)资助.

The Global Solutions of the Compressible Euler Equations With Nonlinear Damping in 3-Dimensions

ZHU Xu-Sheng, LI Fang-E

1.School of Basic Science, East China Jiaotong University, Nanchang, 330013;
2.Xinxiang No.1 High Sschool, Henan Xinxiang, 453000

Received:2013-04-08 Revised:2014-03-17 Online:2014-10-25 Published:2014-10-25
Supported by:
国家自然科学基金(11161021, 61262031)和江西省高校科技落地计划项目(KJLD12067)资助.

摘要/Abstract

摘要：

研究了三维空间中带非线性阻尼项的可压缩欧拉方程组的初值问题. 利用能量估计和傅立叶分析的方法,在初值是常状态附近的一个H³∩L¹中的小扰动时获得了初值问题的解整体存在, 并得到了解在大时间的L², L^∞ 衰减率分别为t^-3/4, t^-3/2, 将线性阻尼的情形推广到了非线性阻尼的情形.

关键词: 可压缩欧拉方程组, 非线性阻尼, 整体经典解, 衰减率

Abstract:

The Cauchy problem for the compressible isentropic Euler equations with nonlinear damping in three space dimensions is investigated in this paper. The global classic solution is obtained provided the initial data is a small perturbation in H³∩L¹ of a constant state by utilizing energy estimates, the L², L^∞ decays rates of the global solution are also obtained by using Fourier transform method, they are t^-3/4, t^-3/2 respectively. Here we have generalized the linear damping case to nonlinear damping case.

Key words: The compressible Euler equations, Nonlinear damping, Global solutions, Decay estimates

中图分类号:

35L45

朱旭生, 李芳娥. 带非线性阻尼项的三维可压缩欧拉方程组的整体解[J]. 数学物理学报, 2014, 34(5): 1111-1122.

ZHU Xu-Sheng, LI Fang-E. The Global Solutions of the Compressible Euler Equations With Nonlinear Damping in 3-Dimensions[J]. Acta mathematica scientia,Series A, 2014, 34(5): 1111-1122.

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