  In this paper, we consider the inviscid limit of the incompressible
Navier-Stokes equations in a smooth, bounded and simply connected domain
$\Omega \subset \mathbb{R}^d, d=2,3$. We prove that for a vortex patch initial
data the weak Leray solutions of the incompressible Navier-Stokes equations
with Navier boundary conditions will converge (locally in time for $d=3$ and
globally in time for $d=2$) to a vortex patch solution of the incompressible
Euler equation as the viscosity vanishes. In view of the results obtained in
[1] and [19] which dealt with the case of the whole space, we derive an almost
optimal convergence rate $(\nu t)^{\frac34-\varepsilon}$ for any small
$\varepsilon>0$ in $L^2$.
