# American Institute of Mathematical Sciences

January  2004, 11(1): 101-112. doi: 10.3934/dcds.2004.11.101

## Remarks on a Smoluchowski equation

 1 Department of Mathematics, The University of Chicago, Chicago, Il 60637 2 Chemical Engineering, PACM and Mathematics, Princeton University, Princeton, NJ 08544, United States 3 Department of Mathematics and Department of Mechanics and Aerospace Engineering, University of California, Irvine, CA 92697, United States

Received  November 2002 Revised  October 2003 Published  April 2004

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.
Citation: Peter Constantin, Ioannis Kevrekidis, E. S. Titi. Remarks on a Smoluchowski equation. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 101-112. doi: 10.3934/dcds.2004.11.101
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