決定在不可壓縮流中的旋轉體

Ru-Lin Kuan; 關汝琳

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37936

完整後設資料紀錄

DC 欄位	值	語言
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
顯示於系所單位：	數學系

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