American Institute of Mathematical Sciences

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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

Yuen-Yick Kwan 1, , Jinhae Park 2, and  Jie Shen 3,

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.
Keywords: Spectral-Galerkin method, Surfactant, Pressure-correction, Weak solution., Navier-Stokes, Instabilities, Existence.
Mathematics Subject Classification: Primary: 76B03, 65M70; Secondary: 76R99, 35K5.
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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