Remarks on a Smoluchowski equation

Peter Constantin, Ioannis Kevrekidis, Edriss S. Titi

Research output: Contribution to journalArticle

46 Scopus citations

Abstract

We study the long time dynamics of a Smoluchowski equation arising in the modeling of nematic liquid crystalline polymers. We prove uniform bounds for the long time average of gradients of the distribution function in terms of the nondimensional parameter characterizing the intensity of the potential. In the two dimensional case we obtain lower and upper bounds for the number of steady states. We prove that the system is dissipative and that the potential serves as unique determining mode of the system.

Original languageEnglish (US)
Pages (from-to)101-112
Number of pages12
JournalDiscrete and Continuous Dynamical Systems
Volume11
Issue number1
DOIs
StatePublished - Jul 2004

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Determining modes
  • Gradient bounds
  • Long time dynamics
  • Nematic liquid crystalline polymers
  • Non-Newtonian fluids
  • Number of steady solutions
  • Rheology
  • Smoluchowski equation

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