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Title: Stability of contact lines in fluids: 2D Navier–Stokes flow
In this paper we study the dynamics of an incompressible viscous fluid evolving in an open-top container in two dimensions. The fluid mechanics are dictated by the Navier–Stokes equations. The upper boundary of the fluid is free and evolves within the container. The fluid is acted upon by a uniform gravitational field, and capillary forces are accounted for along the free boundary. The triple-phase interfaces where the fluid, air above the vessel, and solid vessel wall come in contact are called contact points, and the angles formed at the contact point are called contact angles. The model that we consider integrates boundary conditions that allow for full motion of the contact points and angles. Equilibrium configurations consist of quiescent fluid within a domain whose upper boundary is given as the graph of a function minimizing a gravity-capillary energy functional, subject to a fixed mass constraint. The equilibrium contact angles can take on any values between 0 and\pidepending on the choice of capillary parameters. The main thrust of the paper is the development of a scheme of a priori estimates that show that solutions emanating from data sufficiently close to the equilibrium exist globally in time and decay to equilibrium at an exponential rate.  more » « less
Award ID(s):
2106650
PAR ID:
10568746
Author(s) / Creator(s):
;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Journal of the European Mathematical Society
Volume:
26
Issue:
4
ISSN:
1435-9855
Page Range / eLocation ID:
1445 to 1557
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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