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.
Keywords:a priori estimates, the conjugate inverse problem, interface, Marangoni number.
UDC:
532.5.013.4
Received: 28.02.2019 Received in revised form: 10.03.2019 Accepted: 12.06.2019