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ON THE NONLINEAR STABILITY OF MARANGONI–BÉNARD PROBLEM WITH FREE SURFACE IN THE BOUSSINESQ APPROXIMATION

GIOVANNA GUIDOBONI

Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204-3476, USA

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and

BUM JA JIN

Department of Mathematics, Seoul National Unversity, Seoul 151-742, Korea

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https://doi.org/10.1142/S0218202505003873Cited by:6 (Source: Crossref)

Abstract

We study the Bénard problem in the Boussinesq approximation with upper free surface in the presence of surface tension. Both buoyancy and Marangoni effect are taken into account. Defining a suitable energy functional, we obtain sufficient conditions for nonlinear exponential stability of the rest state.

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