Estimates of the local minimum scale for the incompressible navier-stokes equations navier-stokes equations
Estimates of the local minimum scale for the incompressible navier-stokes equations navier-stokes equations
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不可压缩纳维-斯托克斯方程的局部最小尺度估计 纳维-斯托克斯方程
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
L. Reyna
中科院分区：
文献类型：
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作者：
W. D. Henshaw;H. Kreiss;L. Reyna
我们考虑二维和三维空间中不可压缩Navier-Stokes方程的解。这些方程解的最小尺度是表示最小涡或最尖锐剪切层的长度尺度。我们对空间局部区域的最小尺度进行了估计。我们证明了子域中解的最小尺度与粘度的平方根除以局部最大速度梯度的平方根成正比。并证明了该解在子域上是解析解，且泰勒级数的收敛半径与局部最小标度成正比。
We consider solutions to the incompressible Navier-Stokes equations in two and three space dimensions. The minimum scale of a solution to these equations is the length scale characterizing the smallest eddy or the sharpest shear layer. We derive estimates for the minimum scale for local regions in space. We show that the minimum scale of solutions in a sub-domain is proportional to the square root of the viscosity divided by the square root of the local maximum velocity gradient. We also prove that the solution is analytic in the sub-domain, with the radius of convergence of Taylor series proportional to the local minimum scale.