On the stationary solutions of the Navier-Stokes equations in two dimensions
On the stationary solutions of the Navier-Stokes equations in two dimensions
复制标题
二维纳维-斯托克斯方程的平稳解
DOI：
10.1007/bf00281420
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发表时间：
1967
影响因子：
2.5
通讯作者：
Donald R. Smith
中科院分区：
文献类型：
--
作者：
R. Finn;Donald R. Smith
噢-w。 Vw-Vp= O (0.1) v. w= O 承认在无穷大邻域 o~ 中定义的解，其在~ 8 上实现规定的连续数据 w* 并趋于无穷大处的规定极限 woo [1, 2, 3, 4, 5, 6, 7]，二维解的相应问题仍然悬而未决。据我们所知，数学精度的唯一重要贡献是 LERAY [112]，他证明了存在获得数据 w* 且具有有限狄利克雷积分的解。不幸的是，LERAY 方法对于解满足无穷大条件的意义这一重要问题几乎没有提供任何信息。鉴于斯托克斯悖论，这个问题特别有趣，根据该悖论，线性化方程的相应问题
Aw-w. Vw-Vp= O (0.1) v. w= O admit solutions defined in a neighborhood o~ of infinity, which achieve prescribed continuous data w* on~ 8 and tend to a prescribed limit woo at infinity [1, 2, 3, 4, 5, 6, 7], the corresponding problem for solutions in two dimensions has remained open. To our knowledge, the only significant contribution of mathematical precision is that of LERAY [112, who proved the existence of a solution which achieves the data w* and has finite Dirichlet integral. Unfortunately the method of LERAY yields little information on the important question of the sense in which the solution satisfies the condition at infinity. This question has a particular interest in view of the Stokes paradox, according to which the corresponding problem for the linearized equations