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Konstantina Trivisa
Department of Mathematics, University of Maryland
On the Doi model for the suspension of rod-like molecules
March 9, 2012
3-4 PM, 646 PGH
Abstract
The Doi model for the suspensions of rod-like molecules in a dilute regime
describes the interaction between the orientation of rod-like polymer
molecules on the microscopic scale and the macroscopic properties of the
fluid in which these molecules are contained (cf. Doi and Edwards (1986)).
The orientation distribution of the rods on the microscopic level is
described by a Fokker-Planck-type equation on the sphere, while the fluid
flow is given by the Navier-Stokes equations, which are now enhanced by an
additional macroscopic stress reflecting the orientation of the rods on
the molecular level. Prescribing arbitrarily the initial velocity and the
initial orientation distribution in suitable spaces we establish the
global-in-time existence of a weak solution to our model de fined on a
bounded domain in the three dimensional space. The proof relies on a
quasi-compressible approximation of the pressure, the construction of a
sequence of approximate solutions and the establishment of compactness.
David H. Wagner University of Houston
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Last modified: September 26 2017 - 05:42:22