Rate of strain and vorticity of a Stokeslet ($e_{ij}=\frac{\mathbf{F}\cdot \mathbf{x}}{8\pi \mu r^3}({\delta }_{ij}-3x_i{x}_j/r^2),\mathbf{\omega }=\frac{\mathbf{F}\times \mathbf{x}}{4\pi \mu r^3}$)

Differentiating the Stokeslet gives its rate-of-strain tensor and vorticity, displayed above for $r=|\mathbf{x}|>0$. The pressure is $p=\mathbf{F}\cdot \mathbf{x}/(4\pi r^3)$. Integrating the Newtonian fluid stress tensor over a sphere enclosing the origin gives traction resultant $-\mathbf{F}$, fixing the point-force normalization.