3D viscous incompressible fluid around one thin obstacle

Christophe Lacave (1)

1 IMJ - Institut de Mathématiques de Jussieu

In this article, we consider Leray solutions of the Navier-Stokes equations in the exterior of one obstacle in 3D and we study the asymptotic behavior of these solutions when the obstacle shrinks to a curve or to a surface. In particular, we will prove that a curve has no effect on the motion of a viscous fluid, so it is an erasable singularity for these equations.

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Lacave. 3D viscous incompressible fluid around one thin obstacle. Proceedings of the American Mathematical Society, 2015, 143 (5), pp.2175-2191. ⟨10.1090/S0002-9939-2014-12409-9⟩. ⟨hal-00653694⟩