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

Chérif Amrouche (1) , M. Meslameni (1) , S. Nečasová

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

In this work, we study the linearized Navier-Stokes equations in an exterior domain of R3 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 Lp-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 R3 and the properties in bounded domains. Our approach rests on the use of weighted Sobolev spaces. © 2013 Elsevier Inc.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Chérif Amrouche, M. Meslameni, S. Nečasová. The stationary Oseen equations in an exterior domain: An approach in weighted Sobolev spaces. Journal of Differential Equations, 2014, 256 (6), pp.1955-1986. ⟨10.1016/j.jde.2013.12.010⟩. ⟨hal-00985038⟩