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

2012/12/07 by Gallay, Thierry
#35B35 #35Q30 #76D05 #76D17 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.1582

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 → ∞. This result was obtained in collaboration with Yasunori Maekawa (Kobe University).

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