$L^p$ weighted theory for Navier-Stokes equations in exterior domains

Chérif Amrouche (1) , Huy Hoang Nguyen (1)

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

This paper is devoted to some mathematical questions related to the stationary Navier-Stokes problem in three-dimensional exterior domains. Our approach is based on a combination of properties of Oseen problems in $R^3$ and in exterior domains of $R^3$.

Mots clés: Navier-Stokes equations; Oseen equations; weighted Sobolev spaces; fluid mechanics

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Huy Hoang Nguyen. $L^p$ weighted theory for Navier-Stokes equations in exterior domains. Communications in Mathematical Analysis, 2010, 8 (1), pp.41-69. ⟨hal-00428962⟩