Remarks on a Smoluchowski equation

Peter Constantin; Ioannis Kevrekidis; Edriss S. Titi

doi:10.3934/dcds.2004.11.101

Remarks on a Smoluchowski equation

Peter Constantin, Ioannis Kevrekidis, Edriss S. Titi

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

51 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 language	English (US)
Pages (from-to)	101-112
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems
Volume	11
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2004.11.101
State	Published - 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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10.3934/dcds.2004.11.101

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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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AB - 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.

KW - Determining modes

KW - Gradient bounds

KW - Long time dynamics

KW - Nematic liquid crystalline polymers

KW - Non-Newtonian fluids

KW - Number of steady solutions

KW - Rheology

KW - Smoluchowski equation

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JO - Discrete and Continuous Dynamical Systems

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Remarks on a Smoluchowski equation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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