Asymptotic description of solutions of the exterior Navier Stokes problem in a half space

Matthieu Hillairet (1) , Peter Wittwer (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Département de Physique Théorique

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Matthieu Hillairet, Peter Wittwer. Asymptotic description of solutions of the exterior Navier Stokes problem in a half space. Archive for Rational Mechanics and Analysis, 2012, 205 (2), pp.553-584. ⟨10.1007/s00205-012-0515-6⟩. ⟨hal-00606267⟩