Abstract
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 if the initial data are close to the rest state, i.e. the velocities and the temperature are small and the domain occupied by the liquid is close to a ball, then the problem possesses a unique classical solution which is determined for all positive values of time.
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© 1992 Springer Basel AG
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Solonnikov, V.A. (1992). On an Evolution Problem of Thermocapillary Convection. In: Antontsev, S.N., Khludnev, A.M., Hoffmann, KH. (eds) Free Boundary Problems in Continuum Mechanics. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8627-7_34
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DOI: https://doi.org/10.1007/978-3-0348-8627-7_34
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9705-1
Online ISBN: 978-3-0348-8627-7
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