I've looked in a lot of books on how it would be possible to derive the drag force over a sphere using PDEs. I've also learned in my fluid dynamics class how to derive the drag force of a rotating sphere in steady flow but we didn't use PDEs. Instead, we used superposition and potential flow to find a solution.
I've been able to derive half of the problem mathematically determining that $F_D$ is $4\pi\mu UR^2$ but I can't derive the pressure contribution as substituting my $\frac{\delta u}{\delta r}$ into stokes law results in the pressure contribution being equivalent to zero.
