Viscous diffusion of multiple vortex system

The following analytical solution satisfies the continuity and momentum equations in dimension-less form in the domain $0 \le x, y \le 2\pi$. The solution is periodic in both $x$ and $y$ coordinates.

$$\begin{eqnarray*} u(x,y,t) &=& -\cos x \sin y e^{-2t/Re} \\ v(x,y,t) &=& \sin x... ...e^{-2t/Re} \\ p(x,y,t) &=& -0.25( \cos 2x + \cos 2y) e^{-4t/Re} \end{eqnarray*}$$