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研究生:關汝琳
研究生(外文):Ru-Lin Kuan
論文名稱:決定在不可壓縮流中的旋轉體
論文名稱(外文):Identification of a Rotating Obstacle in anIncompressible Fluid
指導教授:王振男
指導教授(外文):Jenn-Nan Wang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:30
中文關鍵詞:納維-斯托克斯方程旋轉的障礙物反問題不可壓縮流體
外文關鍵詞:Navier-Stokes equationsrotatingobstacleinverse problemincompressible fluid
相關次數:
  • 被引用被引用:0
  • 點閱點閱:215
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  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
我們討論這個問題:在一個不可壓縮流體的流域中,我們能不能確定流體中的旋轉障礙物的位置和形狀?我們只考慮2維跟3維情況。

事實上我們只能解決部分的問題.非旋轉障礙物的確定已經在前輩的文章中完成.但旋轉的情況又更加困難,必須增加其他的條件才能確立。首先,為了簡化我們的問題,我們只考慮旋轉不變的流域。這個意思是說,我們先假設這�堛滷衕鄎�的是繞著z軸旋轉。也就是說,確定一個繞著z軸旋轉的障礙物在繞著z軸旋轉不變的流域(例如:圓柱)中。如果我們給一個流域的邊界值f, f對時間微分不為零且f(x,t)=h(t)g(x),並增加其他保證方程有解的條件,則我們就可以確定這個旋轉中的障礙物。在本文中我們只考慮的方程式線性化的Navier-Stokes方程,若是非線性的Navier-Stokes則需要討論解的存在性及regularity等問題,這個部份由於時間的關係,尚未完全解決,故不納入論文中。
We want to study this problem: Can we determine a rotating unknown obstacle D in an incompressible fluid which is filled with a bounded domain by the velocity
on the boundary of this domain? In fact, we only solve the partial problem. In dimension 3, we assume that a C2 bounded domain possess an axis paralleled with the zaxis and the domain is a circle at any horizontal plane. The unknown obstacle D rotates this axis with angular velocity $omega$ = (0, 0, 1)T . And in dimension 2, we assume that the domain is a circle, and this unknown obstacle rotates this center of this circle with angular velocity $omega$= (0, 0, 1)T . Then, we can identify the location and shape of the two unknown rotating obstacles by the velocity on the boundary of this domain.
口試委員審定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

誌謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Existance of weak solutions . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The continuation property for our equation . . . . . . . . . . . . . . . 20
3 The Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
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