Applied Analysis on the Navier-Stokes Equations and Related Dynamical Systems

纳维-斯托克斯方程和欧拉方程是流体力学的主方程。我们寻找奇点和伪奇点。骄傲人。研究了带有积分约束的Johnson方程和反应扩散方程。通过数值计算解，我们发现存在拓扑简单的解，并且它们仅存在于二维纳维-斯托克斯方程及其密切相关的方程中。计算了渐进水波中流体粒子的轨迹。所谓的斯托克斯漂移已在数学上得到证明。我们的证明比任何其他证明都简单，并且很容易适应数值计算。我们的数值方法使我们不仅能够计算重力波，还能计算毛细管重力波。

The Navier-Stokes equations and the Euler equations are the master equations of the fluid mechanics. We searched for singularity and pseudo singularity. The Proudman. Johnson equation and reaction-diffusion equation with integral constraint were studied. By numerically computing solutions, we found that a topologically simple solutions exists and they exist only in two-dimensional Navier-Stokes equations and those closely related to it.Trajectories of fluid particles in a progressive water-waves were computed. What is called the Stokes drift was proved mathematically. Our proof is simpler than any other proof and easily adapted to the numerical computation. Our numerically method enables us to compute not only the gravity waves but also capillary-gravity waves.