Regularity of coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems (Q883062)

The authors discuss the global regularity of systems describing fluids with particles suspensions. The particles are parameterized by independent microscopic variables \(m\) belonging to a compact, connected, smooth \(d\)-dimensional Riemannian manifold \(M\). The particles are included in a fluid in \(\mathbb{R}^n\), for \(n=2\) obeying the forced Navier-Stokes equations. It is assumed that the density of particles is carried by the time average of the fluid velocity. It is shown that for \(n=2\) the coupled system has smooth solutions at all parameter values.