  In this Note, we prepare an $\varepsilon$-Stokes problem connecting the
Stokes problem and the corresponding pressure-Poisson equation using one
parameter $\varepsilon>0$. We prove that the solution to the
$\varepsilon$-Stokes problem, convergences as $\varepsilon$ tends to 0 or
$\infty$ to the Stokes and pressure-Poisson problem, respectively.
