Solution Of Two-dimensional Incompressible Navier-stokes Equations Of A Vorticity Stream Function Method

This is a summary, which is based on bibliographies [1] [2] [3] [8] [9] [10], always focusing on the equationsIn Chapter 1, we review the background and the vorticity-streamfunction approach for the 2-D incompressible Navier-Stokes equations. In order to explain our problem clearly, in Chapter 2 we provide some preliminaries, which are taken from textbooks([4] [6] [7]), bibliographies([5] [7]) and simple mathematical calculations. In Chapter 3, we summarize by three theorems([8]) to formulate the well-posedness of (*) in sobolev spaces (such as L¹ (R²)∩C^2,λ(R²) , L¹ (R²)∩C(R²), L¹ (R²)), which the initial valueξ₀(x) belongs to. In Chapter 4, we finaly use a difference numerical scheme([10]) to obtain the numerical soultion.