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H^3∩L^1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L^2,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.
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 H^3∩ L^1 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.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2014年第5期1111-1122,共12页
Acta Mathematica Scientia
基金
国家自然科学基金(11161021
61262031)
江西省高校科技落地计划项目(KJLD12067)资助
关键词
可压缩欧拉方程组
非线性阻尼
整体经典解
衰减率
The compressible Euler equations
Nonlinear damping
Global solutions
Decayestimates.
