Finally, we investigate the motion of a general form rigid body with smooth boundary by an incompressible perfect fluid occupying R3 . Due to the domain occupied by the fluid depending on the time, this problem can be transformed into a new systems of the fluid in a fixed domain by the frame attached with the body. With the aid of Kato-Lai's theory, we construct a sequence of successive solutions to this problem in some unform time interval. Then by a fixed point argument, we have proved that the existence, uniqueness and persistence of the regularity for the solutions of original fluid-structure interaction problem. / In the first part, we study the issue of the inviscid limit of the incompressible Navier-Stokes equations on the general smooth domains for completely slip boundary conditions. We verify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in the Prantle's theory. We improve the better regularity for the boundary layer and obtain the uniform Lp--estimates (3 < p ≤ 6) of the remainder. Then we improved these estimates to H 1--estimates. It is shown that the viscous solution converges to the solution of Euler equation in C([0, T]; H1(O)) as the viscosity tends to zero. / In the second part, we consider the non-stationary problems of a class of non-Newtonian fluid which is a power law fluid with p > 3nn+2 in the half space with slip boundary conditions. We present the local pressure estimate with the Navier's slip boundary conditions. Using these estimates and an Linfinity -- truncation method, we can obtain that this system has at least one required weak solution. / In this thesis, we study several issues involving incompressible viscous fluids with the slip boundary conditions and the motions of fluid-solid interactions. / Zang, Aibin. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 128-141). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_344849 |
| Date | January 2011 |
| Contributors | Zang, Aibin., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (141 leaves : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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