The Stationary Oseen equations in an exterior domain: An approach in weighted Sobolev spaces

0427503 - MÚ 2015 RIV US eng J - Journal Article
Amrouche, Ch. - Meslameni, M. - Nečasová, Šárka
The Stationary Oseen equations in an exterior domain: An approach in weighted Sobolev spaces.
Journal of Differential Equations. Roč. 256, č. 6 (2014), s. 1955-1986. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA ČR(CZ) GAP201/11/1304; GA ČR GAP201/10/1920
Institutional support: RVO:67985840
Keywords : Oseen equations * weighted Sobolev spaces * exterior domain
Subject RIV: BA - General Mathematics
Impact factor: 1.680, year: 2014
http://www.sciencedirect.com/science/article/pii/S0022039613005044

In this work, we study the linearized Navier–Stokes equations in an exterior domain of R3R3 at the steady state, that is, the Oseen equations. We are interested in the existence and the uniqueness of weak, strong and very weak solutions in LpLp-theory which makes our work more difficult. Our analysis is based on the principle that linear exterior problems can be solved by combining their properties in the whole space R3R3 and the properties in bounded domains. Our approach rests on the use of weighted Sobolev spaces.
Permanent Link: http://hdl.handle.net/11104/0233031