Abstract
We investigate the Doi model for suspensions of rod–like molecules in the dilute regime. For certain parameter values, the velocity gradient vs. stress relation defined by the stationary and homogeneous flow is not rank–one monotone. We then consider the evolution of possibly large perturbations of stationary flows. We prove that, even in the absence of a microscopic cut–off, discontinuities in the velocity gradient cannot occur in finite time. The proof relies on a novel type of estimate for the Smoluchowski equation.
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Otto, F., Tzavaras, A.E. Continuity of Velocity Gradients in Suspensions of Rod–like Molecules. Commun. Math. Phys. 277, 729–758 (2008). https://doi.org/10.1007/s00220-007-0373-5
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DOI: https://doi.org/10.1007/s00220-007-0373-5