Communications in Mathematical Sciences

Volume 12 (2014)

Number 8

Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rod-like particles

Pages: 1579 – 1601

DOI: https://dx.doi.org/10.4310/CMS.2014.v12.n8.a10

Authors

Xiuqing Chen (School of Sciences, Beijing University of Posts and Telecommunications, Beijing, China; Department of Physics and Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)

Xiaolong Li (School of Sciences, Beijing University of Posts and Telecommunications, Beijing, China)

Jian-Guo Liu (Department of Physics and Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)

Abstract

We investigate a kinetic model for the sedimentation of dilute suspensions of rod-like particles under gravity, deduced by Helzel, Otto, and Tzavaras (2011), which couples the impressible (Navier-)Stokes equation with the Fokker-Planck equation. With a no-flux boundary condition for the distribution function, we establish the existence and uniqueness of a global weak solution to the two dimensional model involving the Stokes equation.

Keywords

Fokker-Planck equation, global weak solution, uniqueness

2010 Mathematics Subject Classification

35K55, 35Q30, 65M06, 76D05

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Published 14 May 2014