Continuity of velocity gradients in suspensions of rod-like molecules

Felix Otto*, Athanasios Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)729-758
Number of pages30
JournalCommunications in Mathematical Physics
Volume277
Issue number3
DOIs
StatePublished - Feb 1 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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