First, we investigate the steady Euler flows through a general 3-D axially symmetric infinitely long nozzles without irrotationality. Global existence and uniqueness of subsonic solution are established, when the variation of Bernoulli's function in the upstream is sufficiently small and mass flux has an upper critical value. / Second, we concerns the following transonic shock phenomena in a class of de Laval nozzles with porous medium posed by Courant-Friedrichs: Given a appropriately large receiver pressure pr, if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes pr. We investigate this problem for the full Euler equations, the stability of the transonic shock is proved when the upstream supersonic flow is a small steady perturbation of the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation. / Duan, Ben. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 125-137). / 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_344623 |
| Date | January 2010 |
| Contributors | Duan, Ben., 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 (ii, 137 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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