Athanasios Tzavaras
Department of Mathematics
University of Maryland

Abstract: We discuss modeling aspects and the existence theory for kinetic models describing dilute suspensions of rigid rods. The model consists of a coupled Fokker-Planck equation describing the evolution of a micro-scale together with Stokes flow for the motion of the solvent. For certain parameter values, the velocity gradient versus stress relation defined by the stationary and homogeneous flow is not rank--one monotone. We consider the evolution of possibly large perturbations of stationary flows and prove that, even in absence of a microscopic cut--off, discontinuities in the velocity gradient cannot occur in finite time.