Abstract
In the present paper, we investigate the scalar Oseen equation in a two-dimensional exterior domain Ω, with Dirichlet boundary condition. This problem represents a linearized form of the steady Navier-Stokes equations. In order to better control the behavior at infinity of functions, the use of weighted Sobolev spaces as a functional framework turns out to be adequate. The established results are related to the existence and the uniqueness of weak solutions on Lp-theory for any real 1<p<∞. Our analysis is mainly based on the principle that linear exterior problems can be solved by combining their properties in bounded domains which are also established in this paper and their properties well known in the whole space R2.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
