Dynamics of Partial Differential Equations
Volume 8 (2011)
Long-time asymptotics of the second grade fluid equations on R²
Pages: 185 – 223
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.
second grade fluid system, weighted Sobolev spaces, Oseen vortex
2010 Mathematics Subject Classification
Primary 35-xx. Secondary 76-xx.