 Gyrotactic orientation Fokker-Planck equation

For orientation probability density $f$ on the unit sphere, deterministic drift $\dot{\mathbf{p}}$ and isotropic rotational diffusion coefficient $D_R$ give ${\partial }_{t}f+{\nabla }_p\cdot (f\dot{\mathbf{p}}-D_R{\nabla }_{p}f)=0$. The derivatives are tangential to the sphere, and normalization is $\int fd\Omega =1$. The spherical divergence of $\mathbf{k}-p_3\mathbf{p}$ is $-2p_3$.