Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain

Abstract

We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as $t\to \infty$. This result was obtained in collaboration with Yasunori Maekawa (Kobe University).

This is a non-technical presentation of the results obtained in arXiv:1202.4969, including simplified proofs and additional information on the convergence of vorticity

References in corpus (2)

• Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain
• Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity