Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain

Details Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain

2011-07-11

arxiv.org/abs/1107.2054v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

We consider the 2D incompressible Navier-Stokes equations with Dirichlet boundary condition in the exterior of one obstacle. Assuming that the circulation at infinity of the velocity is sufficiently small, we prove that the large time behavior of the corresponding solution to the initial-boundary value problem is described by the Lamb-Oseen vortex. The later is the well-known explicit self-similar solution to the Navier-Stokes system in the whole space $\R^2$.

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