标题： 二维Navier Stokes方程的傅里叶解，具有周期性边界条件和不可压缩流动 显示英文标题

标题： Fourier solution of two-dimensional Navier Stokes equation with periodic boundary conditions and incompressible flow

摘要： 通过用复数傅里叶基向量表示流体速度的x和y分量，得到了二维纳维-斯托克斯方程在周期性边界条件下的近似解。 所选择的基向量空间是有限的，以允许进行数值计算，但其大小是可变的。 通过比较随着所选向量空间大小变化而得到的近似解，可以外推到无限基向量空间。 结果表明，当初始速度和时间t超过一定限制时，对于某些初始速度配置，这样的解（使用完整的基向量空间，理论上应给出精确解）将失效。 显示英文摘要

摘要： An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.