Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 3

Long-time asymptotics of the second grade fluid equations on R²

Pages: 185 – 223

DOI: https://dx.doi.org/10.4310/DPDE.2011.v8.n3.a2

Author

Basma Jaffal-Mourtada (Laboratoire de Mathématiques, Université Paris-Sud, Orsay, France)

Abstract

We study the large time behavior of solutions of the second grade fluid system in the space R². Using scaled variables and introducing several functionals in weighted Sobolev spaces, we prove that the solution of the second grade fluid equations converges to the Oseen vortex, if the initial data are small enough. We also give an estimate of the rate of convergence.

Keywords

second grade fluid system, weighted Sobolev spaces, Oseen vortex

2010 Mathematics Subject Classification

Primary 35-xx. Secondary 76-xx.

Published 15 September 2011