Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions

We prove the existence of the global weak entropy solution to the Doi-Saintillan-Shelley model for active and passive rod-like particle suspensions, which couples a Fokker-Planck equation with the incompressible Navier-Stokes or Stokes equation, under the no-flux boundary conditions, L-2(Omega; L-1 (Sd-1)) initial data, and finite initial entropy for the particle distribution function in two and three dimensions. Furthermore, for the model with the Stoke equation, we obtain the global L-2(Omega x Sd-1) weak solution in two and three dimensions and the uniqueness in two dimension. (C) 2013 Elsevier Inc. All rights reserved.