  In this article, we consider 2D second grade fluid equations in exterior
domain with Dirichlet boundary conditions. For initial data $\boldsymbol{u}_0
\in \boldsymbol{H}^3(\Omega)$, the system is shown to be global well-posed.
Furthermore, for arbitrary $T > 0$ and $s \geq 3$, we prove that the solution
belongs to $L^\infty([0, T]; \boldsymbol{H}^s(\Omega))$ provided that
$\boldsymbol{u}_0$ is in $\boldsymbol{H}^s(\Omega)$.
