On a coupled Kuramoto-Sivashinsky and Ginzburg-Landau-type model for the Marangoni convection

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) + 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. This work sets the foundation for further study of this model. (C) 1997 American Institute of Physics.