Ladyzhenskaya流体力学方程组的确定模与确定结点个数估计

Determining Modes and Determining Nodes to the Fluid Flow of Ladyzhenskaya Model

论文给出了二维有界区域上Ladyzhenskaya流体力学方程组的确定模与确定结点的个数估计.结果表明若该方程组的任意两个弱解的前有限个傅立叶模有相同的渐近行为,则这两个解就具有相同的渐近行为;若该方程组的任意两个强解在有限个空间中的点上有相同的渐近行为,则这两个解几乎在整个空间上具有相同的渐近行为.

This article estimates the finite number of determining modes and determining nodes for the fluid flow of Ladyzhenskaya model on two-dimensional bounded smooth domains. The finite number of determining modes implies that the solutions of the addressed fluids are determined completely by their first finite number of Fourier modes. The determining nodes reveals that whenever two different solutions of the fluid have the same asymptotic behavior at finite number of points in the physical space, then they also possess the same asymptotic behavior at almost everywhere points of the physical space.