The 3D Navier-Stokes Problem

被引：70
|
作者：
Doering, Charles R. [1 ,2 ]
机构：
[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
[2] Univ Michigan, Dept Phys, Ann Arbor, MI 48109 USA
来源：
ANNUAL REVIEW OF FLUID MECHANICS | 2009年 / 41卷
基金：
美国国家科学基金会;
关键词：
incompressible Newtonian fluid mechanics; initial value problem; uniqueness of solutions; regularity of solutions; vortex stretching; turbulence; ENERGY-DISSIPATION RATE; WEAK SOLUTIONS; REGULARITY; EQUATIONS; FLOW;
D O I：
10.1146/annurev.fluid.010908.165218
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
It is not known whether the three-dimensional (3 D) incompressible Navier-Stokes equations possess unique smooth (continuously differentiable) solutions at high Reynolds numbers. This problem is quite important for basic science, practical applications, and numerical computations. This review presents a selective survey of die current state of die mathematical theory, focusing oil the technical source of difficulties encountered with the construction of smooth solutions. It also highlights physical phenomena behind the mathematical challenges.
引用
收藏
页码：109 / 128
页数：20
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