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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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Bang, Jeaheang. Stationary Navier-Stokes equations in an exterior domain, and some integral identities for Euler and Navier-Stokes equations. Retrieved from https://doi.org/doi:10.7282/t3-f1w0-6039

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TitleStationary Navier-Stokes equations in an exterior domain, and some integral identities for Euler and Navier-Stokes equations
NameBang, Jeaheang (author); Li, YanYan (chair); Han, Zheng-Chao (internal member); Kriventsov, Dennis (internal member); Chae, Dongho (outside member); Rutgers University; School of Graduate Studies
Date Created2021
Other Date2021-05 (degree)
SubjectMathematics, Navier-Stokes equations
Extent1 online resource (vi, 140 pages)
DescriptionWe 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.
NotePh.D.
NoteIncludes bibliographical references
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-f1w0-6039
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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