Abstract
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for horizontally periodic flows. This problem gives rise to flat but vertically oscillating equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of these equilibria in certain parameter regimes. We prove that both with and without surface tension there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t = 0 t = 0 give rise to global-in-time solutions that decay to equilibrium at an identified quantitative rate.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
