Free boundary problem for a viscous heat-conducting flow with surface tension

Abstract

In the paper the equations describing the motion of a drop of a viscous heat-conducting capillary fluid bounded by a free surface are examined. Assuming that the viscosity coefficients, the coefficient of heat-conductivity, the pressue and the specific heat at constant volume of the fluid depend on its density and temperature we prove the existence of a global in time solution which is close to a constant state for any moment of time.