The 3D Incompressible Euler Equations with a Passive Scalar: A Road to Blow-Up?

被引：8
作者：
Gibbon, John D. [1 ]
Titi, Edriss S. [2 ,3 ,4 ]
机构：
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England
[2] Weizmann Inst Sci, Dept Comp Sci & Appl Math, IL-76100 Rehovot, Israel
[3] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA
[4] Univ Calif Irvine, Dept Mech & Aerosp Engn, Irvine, CA 92697 USA
来源：
JOURNAL OF NONLINEAR SCIENCE | 2013年 / 23卷 / 06期
基金：
美国国家科学基金会;
关键词：
Incompressible Euler equations; Passive scalar; No-normal-flow boundary conditions; Singularity; Null point; POTENTIAL VORTICITY; WEAK SOLUTIONS; TURBULENCE; PRINCIPLE; HYDRODYNAMICS; EXISTENCE;
D O I：
10.1007/s00332-013-9175-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The three-dimensional incompressible Euler equations with a passive scalar theta are considered in a smooth domain with no-normal-flow boundary conditions . It is shown that smooth solutions blow up in a finite time if a null (zero) point develops in the vector B=a double dagger qxa double dagger theta, provided B has no null points initially: is the vorticity and q=omega a <...a double dagger theta is a potential vorticity. The presence of the passive scalar concentration theta is an essential component of this criterion in detecting the formation of a singularity. The problem is discussed in the light of a kinematic result by Graham and Henyey (Phys. Fluids 12:744-746, 2000) on the non-existence of Clebsch potentials in the neighbourhood of null points.
引用
收藏
页码：993 / 1000
页数：8
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