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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
50/2000

Model of a viscous layer deformation by thermocapillary forces

Vladislav V. Pukhnachev

Abstract

Three-dimensional nonstationary flow of viscous incompressible liquid is investigated in a layer generated by nonuniform distribution of temperature on its free boundaries. If the temperature given on the layer boundaries is quadratically dependent on homogeneous coordinates, the external mass forces are absent and the motion arises from the rest state then the problem with free boundaries for the Navier-Stokes equations has the "exact" solution determined from system of equations with two independent variables. Here the free boundaries of the layer remain parallel planes and the distance between them must be also determined. Formulated in present paper are the conditions of both the unique solvability of the reduced problem on the whole in time and the collapse of the solution in finite time. Moreover studied in this paper are qualitative properties of the solution such as its behaviour at large time in the case of global solvability of the problem and the asymptotics of the solution near the collapse moment in the opposite case.

Received:
Aug 29, 2000
Published:
Aug 29, 2000

Related publications

inJournal
2002 Repository Open Access
Vladislav V. Pukhnachov

Model of a viscous layer deformation by thermocapillary forces

In: European journal of applied mathematics, 13 (2002) 2, pp. 205-224