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# Xiuqing Chen : Global weak solution for kinetic models of active swimming and passive suspensions

We investigate two kinetic models for active suspensions of rod-like and ellipsoidal particles, and passive suspensions of dumbbell beads dimmers, which couple a Fokker-Planck equation to the incompressible Navier-Stokes or Stokes equation. By applying cut-off techniques in the approximate problems and using compactness argument, we prove the existence of the global weak solutions with finite (relative) entropy for the two and three dimensional models. For the second model, we establish a new compact embedding theorem of weighted spaces which is the key in the compactness argument. (Joint work with Jian-Guo Liu)

**Category**: Applied Math and Analysis**Duration**: 01:34:44**Date**: February 13, 2012 at 4:25 PM**Views**: 105-
**Tags:**seminar, Applied Math And Analysis Seminar

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