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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37936Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 王振男(Jenn-Nan Wang) | |
| dc.contributor.author | Ru-Lin Kuan | en |
| dc.contributor.author | 關汝琳 | zh_TW |
| dc.date.accessioned | 2021-06-13T15:52:07Z | - |
| dc.date.available | 2008-07-03 | |
| dc.date.copyright | 2008-07-03 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-06-25 | |
| dc.identifier.citation | [1] C. Alvarez, C. Conca, L. Friz, O. Kavian and J. H. Ortega, Identification of
Immersed Obstacles Via Boundary Measurements, Inverse Problems 21 (2005), 1531-1552. [2] Toshiaki Hishida, An Existence Theorem for the Navier-Stokes Flow in the Exterior of Rotating Obstacle, Arch. Rational Mech. Anal. 150 (1999), 307- 348. [3] H.P.Greenspan, The Theory of Rotating Fluids, Cambridge University Press, London, 1969. [4] Giovanni P. Galdi et. al(Eds.), Fundamental Directions in Mathematical Fluid Mechanics, Birkhauser, Basel, 2000. [5] Roger Temam, Navier-Stokes equations : theory and numerical analysis, North- Holland Pub. Co., New York, 1977. [6] Fabre C. and Lebeau G., Prolongement unique des solutions de l’´equation de Stokes, Commun. Part. Diff. Eqns 21 (1996), 573-596. [7] Jin Kim Tu and Chang Qianshun, Remark on unique continuation of solutions to the Stokes and the Navier-Stokes equations, Acta Math. Sci. Ser. B Engl. Ed. 25 (2005), no. 4, 594-598. [8] He, Cheng, The initial-boundary value problem for Navier-Stokes equations, Acta Math. Sin. (Engl. Ser.) 15 (1999), no. 2, 153–164. [9] O A Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, 1969. [10] Tosio Kato and Gustavo Ponce, Commutater estimates and the Euler and Navier-Stokes equations,Communications on Pure and Applied Mathematics 41 (1988), 891-907. [11] Galdi, Giovanni P, An introduction to the mathematical theory of the Navier- Stokes equations. Vol. I. Linearized steady problems, Springer Tracts in Natural Philosophy, 38. Springer-Verlag, New York, 1994. [12] Galdi, Giovanni P, An introduction to the mathematical theory of the Navier- Stokes equations. Vol. II. Nonlinear steady problems, Springer Tracts in Natural Philosophy, 39. Springer-Verlag, New York, 1994. [13] Evans, Lawrence C, Partial differential equations. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 1998. [14] G. Stampacchia, Equations elliptiques du second ordre `a coefficients discontinus , Presses de I’Universit´e de Montr´eal, 1996. [15] J. L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, Springer-Verlag, New York, 1972. [16] Peter D. Lax, Functional Analysis, John Wiley & Sons, Canada. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37936 | - |
| dc.description.abstract | 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,我們先假設這裏的旋轉指的是繞著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。 | zh_TW |
| dc.description.abstract | 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. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T15:52:07Z (GMT). No. of bitstreams: 1 ntu-97-R94221011-1.pdf: 466954 bytes, checksum: a7712962419c09422fa32a81b18c5d58 (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | 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 | |
| dc.language.iso | en | |
| dc.subject | 旋轉的 | zh_TW |
| dc.subject | 納維-斯托克斯方程 | zh_TW |
| dc.subject | 障礙物 | zh_TW |
| dc.subject | 反問題 | zh_TW |
| dc.subject | 不可壓縮流體 | zh_TW |
| dc.subject | incompressible fluid | en |
| dc.subject | Navier-Stokes equations | en |
| dc.subject | rotating | en |
| dc.subject | obstacle | en |
| dc.subject | inverse problem | en |
| dc.title | 決定在不可壓縮流中的旋轉體 | zh_TW |
| dc.title | Identification of a Rotating Obstacle in an
Incompressible Fluid | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林太家(Tai-Chia Lin),林景隆 | |
| dc.subject.keyword | 納維-斯托克斯方程,旋轉的,障礙物,反問題,不可壓縮流體, | zh_TW |
| dc.subject.keyword | Navier-Stokes equations,rotating,obstacle,inverse problem,incompressible fluid, | en |
| dc.relation.page | 30 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-06-25 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| ntu-97-1.pdf Restricted Access | 456.01 kB | Adobe PDF |
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