A Numerically Based Existence Theorem for the Navier-Stokes Equations
A Numerically Based Existence Theorem for the Navier-Stokes Equations
复制标题
纳维-斯托克斯方程的数值存在定理
DOI：
10.1007/s000210050002
复制
发表时间：
1999
影响因子：
1.3
通讯作者：
W. Xie
中科院分区：
文献类型：
--
作者：
J. G. Heywood;W. Nagata;W. Xie
我们最近实验了一个新的频谱代码的空间周期非定常Navier-Stokes方程，找到了大量的显然是稳定的，周期性的和混乱的解决方案，从动力系统理论的角度来看，这似乎很有趣。这激发了我们对证明微分方程严格解的存在性的一般问题的兴趣，这些严格解对应于数值实验的计算结果。在本文中，我们分析了我们的一个实验的数值结果。计算结果似乎近似于似乎是一个不稳定的稳定的解决方案。我们的目的是提供一个严格的后验分析，证明确实存在一个相应的严格接近解，并且它是稳定的。我们的方法是基于显示计算的解决方案满足的标准，这意味着收敛的不动点迭代，在适当的函数空间的存在定理，使用计算的解决方案作为起始值
We have recently experimented with a new spectral code for the spatially-periodic nonstationary Navier-Stokes equations, finding a plethora of apparently steady, periodic and chaotic solutions which seem interesting from the point of view of dynamical systems theory. This has stimulated our interest in the general problem of proving the existence of strict solutions of differential equations, that correspond to the computational results of numerical experiments. In this paper we analyze the numerical results of one of our experiments. The computational results appear to approximate what seems to be an unstable steady solution. Our objective is to provide a rigorous a-posteriori analysis, proving that there does indeed exist a corresponding close by strict solution, and that it is steady. Our method is based on showing that the computed solution satisfies criteria which imply the convergence of a fixed point iteration, in appropriate function spaces for an existence theorem, using the computed solution as the starting value