A Priori Estimates of the Conjugate Problem Describing an Axisymmetric Thermocapillary Motion for Small Marangoni Number

Abstract

This paper is devoted to the study of equations solution describing the axisymmetric motion of a viscous heat-conducting liquid. The motion is interpreted as a two-layer flow of viscous heat-conducting liquids in a cylinder with a solid wall and a common movable non-deformable interface. From a mathematical point of view, the arising initial-boundary value problem is nonlinear and inverse. Under certain assumptions concerning to apply the problem is replaced by a linear one. As a result, the unimprovable uniform priori estimates for solutions of the problems posed are obtained.