# Yoshiaki Teramoto : Benard-Marangoni problem of heat convection with free surface

When a fluid layer is heated from below with temperature larger than a certain critical value, the convective motion appears in the fluid. The convection caused by the thermocapillary effect is called Benard-Marangoni heat convection. The thermocapillary effect is the dependence of the surface tension on the temperature. Near a hot spot on a free surface of fluid a thermocapillary tangential stress generates a fluid motion. In this talk the mathematical model system for this convection is explained. The Oberbeck-Boussinesq approximation is used for the system and the upper boundary is a free surface with surface tension which depends on the temperature. After formulating the linearized problem around the conductive state, we derive the resolvent estimates which guarantee the sectorial property. Stationary and Hopf bifurcations (periodic solutions) are proved to exist depending on the parameters (Raylegh and Marangoni numbers).

**Category**: Applied Math and Analysis**Duration**: 01:34:55**Date**: August 30, 2010 at 4:25 PM**Views**: 103-
**Tags:**seminar, Applied Math And Analysis Seminar

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