二維渦度方程及其應用

The Two-dimensional Vorticity Equation and its Application

林懌(Lin, I)

指導教授 ： 江金城

國立清華大學/理學院/數學系/碩士(2015年)

摘要

本論文是針對 Giga 及 Kambe 在渦度方程上研究結果的整理。在本論文中，我們將從描述帶有黏性且不可壓縮的流體運動的 Navier-Stokes 方程出發導出渦度方程。建基於渦度方程解的存在與唯一性，我們證明其解的漸進定理，即當時間足夠大時解的漸進行為。然後討論此漸進定理的一個應用。

關鍵字

渦度 ； 流體

並列摘要

This thesis is a survey of research result of Giga and Kambe on the vorticity equation. In this thesis, we start with the Navier-Stokes equations, which describe the incompressible viscous flows in fluid mechanics, then the vorticity equation is derived from them. Based on the existence and uniqueness for the solution of the vorticity equation, we have the asymptotic formula for the solution which means the solution will approach the fundamental solution of the heat equation as time is large enough. Then we discuss an application of this asymptotic formula.

並列關鍵字

Navier-Stokes

參考文獻

Euler equations”. Arch. Rational Mech. Anal., 128, 329-358

[2] Mi-Ho Giga, Yoshikazu Giga, and Jürgen Saal (2010), “Nonlinear Partial

Differential Equations: Asymptotic Behavior of Solutions and Self-Similar

Solutions”. Springer

[4] T. Kambe (1984), “Axisymmetric vortex solution of Navier-Stokes equation”.