Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations

被引：13
|
作者：
Hou, Thomas Y. [1 ]
Liu, Pengfei [1 ]
机构：
[1] CALTECH, Comp Math Sci, Pasadena, CA 91125 USA
来源：
RESEARCH IN THE MATHEMATICAL SCIENCES | 2015年 / 2卷 / 01期
关键词：
Euler Equation; Singular Solution; Interval Arithmetic; Decay Condition; Local Truncation Error;
D O I：
10.1186/s40687-015-0021-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which approximates the dynamics of the Euler equations on the solid boundary of a cylindrical domain. We prove the existence of a discrete family of self-similar profiles for this model and analyze their far-field properties. The self-similar profiles we find are consistent with direct simulation of the model and enjoy some stability property.
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页数：26
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