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Stationary Navier-Stokes equations in an exterior domain, and some integral identities for Euler and Navier-Stokes equations
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Title
Stationary Navier-Stokes equations in an exterior domain, and some integral identities for Euler and Navier-Stokes equations
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Jeaheang
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Jeaheang Bang
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Li
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YanYan Li
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chair
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Han
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Zheng-Chao
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Zheng-Chao Han
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Kriventsov
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Dennis
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Dennis Kriventsov
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Advisory Committee
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Chae
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Dongho
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Dongho Chae
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Rutgers University
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School of Graduate Studies
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theses
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ETD doctoral
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2021
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2021-05
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English
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We study: 1) the stationary Navier-Stokes equations in a two-dimensional exterior domain, 2) some integral identities for the Euler and the Navier-Stokes equations. For the first topic, we consider the non-homogenous boundary value problem in a two-dimensional exterior domain together with a prescribed condition at infinity and establish existence of a solution to the problem provided that the boundary value on the boundary of the domain is close to a potential flow; this assumption allows some large boundary value. Indeed, we utilize results of Galdi in 2004 on the Oseen equations, a linearization around a constant nonzero vector. Then we apply ideas used in Russo and Starita's work (in 2008) in three dimension, which is to perturb around a potential flow; in conjunction with the compactness of some linear operator related to the Oseen equations, which is a result again of Galdi in 2004.
For the second topic, Dobrokhotov and Shafarevich in 1994 proved some integral identities for the Euler and Navier-Stokes equations. Chae in 2012 proved these integral identities on a hyperplane for a weak solution with some integrability assumptions on the solution. In this thesis, we prove the integral identities on a hyperplane with some different integrability assumptions. It also furnishes a Liouville type theorem as an immediate application, providing a different approach to some of the results of Hamel and Nadirashvili in 2017, 2019, Chae and Constantin in 2015.
For the second topic, Dobrokhotov and Shafarevich in 1994 proved some integral identities for the Euler and Navier-Stokes equations. Chae in 2012 proved these integral identities on a hyperplane for a weak solution with some integrability assumptions on the solution. In this thesis, we prove the integral identities on a hyperplane with some different integrability assumptions. It also furnishes a Liouville type theorem as an immediate application, providing a different approach to some of the results of Hamel and Nadirashvili in 2017, 2019, Chae and Constantin in 2015.
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Mathematics
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Navier-Stokes equations
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Rutgers University Electronic Theses and Dissertations
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1 online resource (vi, 140 pages)
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Ph.D.
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Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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doi:10.7282/t3-f1w0-6039
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The author owns the copyright to this work.
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Jeaheang
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2021-03-30 21:18:39
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Jeaheang Bang
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Rutgers University. School of Graduate Studies
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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