On the stationary Oseen equations in exterior domains
- 발행기관 서강대학교 일반대학원
- 지도교수 김현석
- 발행년도 2016
- 학위수여년월 2016. 8
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000060019
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
In this thesis, we study the stationary Oseen system (O) and rotating Oseen system (RO) on exterior smooth domains in R^3. The systems are linearized versions of the stationary Navier-Stokes flows on exterior domains. Our main results are the existence and uniqueness of weak and very weak solutions of the two systems satisfying appropriate estimates. We first prove the uniqueness of very weak solutions. Then existence results for very weak solutions of (O) and (RO) are deduced by a duality argument from our existence results for strong solutions of (O) and (RO), respectively. Using these results, we finally establish the complete D^{1,r}-results for weak solutions of the two systems, where 4/3 < r < 4. Here D^{1,r} is the homogeneous Sobolev space.
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