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arXiv math/0610086math.AP
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周期Navier-Stokes流的收敛性

On the convergence of periodic Navier-Stokes flows

David T. Purvance

摘要:

将三维空间周期斯托克斯方程转化为非线性矩阵微分方程.当假定流动是具有未知波数系数的时间序列时,则该周期性纳维尔-斯托克斯矩阵微分方程中的矩阵变为矩阵的时间序列。以这种方式设置,任何流的未知波数系数可以递归地从表示任何初始流的零阶系数开始求解。当时间序列中的所有矩阵可交换时,流的未知系数也表示对初始流进行运算的稳定矩阵指数积的泰勒展开。本文证明了当用一般解的非交换矩阵来估计这些界时,解的系数收敛于这些有界泰勒系数。

英文摘要:

The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes matrix differential equation becomes a time series of matrices. Posed in this way, any flow's unknown wavenumber coefficients can be solved for recursively beginning with the zeroth-order coefficient representing any initial flow. When all matrices in the time series commute, a flow's unknown coefficients also represent the Taylor expansion of a stable matrix exponential product operating on the initial flow. This paper argues that a solution's coefficients converge to these bounded Taylor coefficients when these bounds are evaluated with a general solution's noncommutative matrices.

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