Stability of Equilibrium Shapes in Some Free Boundary Problems Involving Fluids

Gieri Simonett () and Mathias Wilke ()
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Gieri Simonett: Vanderbilt University, Department of Mathematics
Mathias Wilke: Universität Regensburg, Fakultät für Mathematik

Chapter 25 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 1221-1265 from Springer

Abstract: Abstract In this chapter the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes flows. In all three situations, the equilibrium states in the absence of outer forces are characterized and their stability properties are analyzed. It is shown that the equilibrium states correspond to the critical points of a natural physical or geometric functional (entropy, available energy, surface area) constrained by the pertinent conserved quantities (total energy, phase volumes). Moreover, it is shown that solutions which do not develop singularities exist globally and converge to an equilibrium state.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13344-7_28

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DOI: 10.1007/978-3-319-13344-7_28

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