### 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.

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.

#### Keywords

Free boundary; surface tension; compressible viscous heat-conducting fluid; global existence

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