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Hydrodynamic limits of the Navier-Stokes equations. / CUHK electronic theses & dissertations collection

Next, we consider that the fluids are isentropic and the domain is also bounded, smooth, simply connected in R2 . We show that the estimates are uniform in all time if the smallness assumption on the initial data is prescribed. It follows that the solutions of compressible Navier-Stokes equations converge to the incompressible ones uniformly in both spatial and temporal variables as the Mach number vanishes. / This thesis deals with the low Mach number limit of the compressible Navier-Stokes equations. It is to verify that the compressible fluids become incompressible as Mach number tends to zero. In another words, the pressure due to compression can be neglected. This is a singular limit. / We will show that, as the Mach number tends to zero, the local smooth solutions of compressible Navier-Stokes equations with zero thermal conductivity coefficient converge strongly to the solutions of incompressible Navier-Stokes equations, provided that the initial data satisfy the "bounded derivative conditions". The key point, which is one of our main contributions, is the uniform high norm estimates in Mach number. We will study two cases. The first case is that, the domain is a finite interval and the boundary condition for the velocity is no-slip. In the second case, the domain is bounded, smooth, and simply connected in R2 . The boundary condition for the velocity is replaced by the slip-type's, thus the vorticity and the divergence of velocity can be estimated separately. / Ou, Yaobin. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3546. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 107-111). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_344265
Date January 2008
ContributorsOu, Yaobin., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, theses
Formatelectronic resource, microform, microfiche, 1 online resource (vi, 111 leaves : ill.)
RightsUse 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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