96-350 Duan, J., Bu, C., Gao, H. and Taboada, M.

On a Coupled Kuramoto-Sivashinsky and Ginzburg-Landau Type Model for the Marangoni Convection (198K, PostScript File) Jul 29, 96

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Abstract. The surface tension driven Marangoni convection is an interesting pattern formation system. The ``primitive" governing equations are too complicated to be investigated analytically. In this paper, the authors consider a simplified model for this system. This simplified model is in the form of coupled Kuramoto-Sivashinsky and Ginzburg-Landau type partial differential equations. The authors prove the existence and uniqueness of global solutions of this simplified mathematical model, under the condition that the Marangoni number $Ma > Ma_c +\frac{k}{2^5}$, where $Ma_c$ is the critical Marangoni number at which the trivial stationary state becomes linearly unstable, and $k$ is a positive constant related to other system parameters. The authors use the contraction mapping principle in the proof as the usual semigroup method does not apply directly to this system. This work sets the foundation for further study of this model.

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