Solonnikov, V. A. On an evolution problem of thermocapillary convection. (English) Zbl 0756.76076 Matematiche 46, No. 1, 449-460 (1991). We consider a free boundary problem of incompressible viscous flow governing the motion of an isolated liquid mass. The liquid is subjected to capillary forces at the boundary, and the coefficient of the surface tension depends on the temperature satisfying the heat equation with convection and dissipation terms. It is shown that this problem is solvable in a certain finite time interval, however, if the data are close to the rest state, the solution can be extended to the interval \(t>0\). MSC: 76R10 Free convection 76D45 Capillarity (surface tension) for incompressible viscous fluids 35Q35 PDEs in connection with fluid mechanics 80A20 Heat and mass transfer, heat flow (MSC2010) Keywords:heat equation with dissipation terms; isolated liquid mass; finite time interval PDFBibTeX XMLCite \textit{V. A. Solonnikov}, Matematiche 46, No. 1, 449--460 (1991; Zbl 0756.76076)