# American Institute of Mathematical Sciences

March  2010, 28(1): 181-197. doi: 10.3934/dcds.2010.28.181

## A mathematical and numerical study of incompressible flows with a surfactant monolayer

 1 Center for Computational Science, Tulane University, New Orleans, LA 70118, United States 2 Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067 3 Department of Mathematics, Purdue University, West Lafayette, IN 47907

Received  March 2010 Revised  March 2010 Published  April 2010

We consider in this paper a mathematical model for the incompressible flows with a surfactant monolayer. The presence of surfactant gives rise to coupling surface terms which make the analysis and simulation challenging. We study the well-posedness of this coupled system of PDEs with physically relevant boundary conditions, as well as the stability of a numerical scheme. We also preform numerical simulations by a fast-spectral method and use it to study the effect of surfactant concentration on the motion of an incompressible fluid in a cylinder.
Citation: Yuen-Yick Kwan, Jinhae Park, Jie Shen. A mathematical and numerical study of incompressible flows with a surfactant monolayer. Discrete & Continuous Dynamical Systems, 2010, 28 (1) : 181-197. doi: 10.3934/dcds.2010.28.181
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