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, L2(Ω;L1(Sd-1)) initial data, and finite initial entropy for the particle distribution function in two and three dimensions. Furthermore, for the model with the Stokes equation, we obtain the global L2(Ω×Sd-1) weak solution in two and three dimensions and the uniqueness in two dimension. © 2013 Elsevier Inc..
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