Long time behavior of solutions to the 3D compressible Euler equations with damping

被引:196
作者
Sideris, TC [1 ]
Thomases, B
Wang, DH
机构
[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
基金
美国国家科学基金会;
关键词
Euler equations; damping; global smooth solutions; existence; decay; singularities;
D O I
10.1081/PDE-120020497
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum norm to the constant background state at a rate of t(-3/2). While the fluid vorticity decays to zero exponentially fast in time, the full solution does not decay exponentially. Formation of singularities is also exhibited for large data.
引用
收藏
页码:795 / 816
页数:22
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