Asymptotic Description of Solutions of the Planar Exterior Navier–Stokes Problem in a Half Space
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- Hillairet, M. & Wittwer, P. Arch Rational Mech Anal (2012) 205: 553. doi:10.1007/s00205-012-0515-6
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 a planar 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.