Nonlinear Rayleigh–Taylor instability for the two-phase Euler equations with surface tension. (June 2019)

• Record Type: Journal Article
• Authors: Lian, Jiali
• Is Part Of: Nonlinear analysis. Volume 183(2019)
• Page Start: 1
• Page End: 28
• Publication Date: 2019-06
• Subjects: 35Q31 -- 35Q35 -- 35R35 -- 76B15 -- 76E17; Euler -- Free boundary -- Two-phase -- Rayleigh–Taylor instability -- Surface tension; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.12.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the free boundary problem for two layers of immiscible, inviscid, incompressible fluid in a uniform gravitational field. The surface tension at the free interface between the two fluids is included so as to exclude the Kelvin–Helmholtz instability, while the upper fluid is assumed to be heavier than the lower fluid so that the fluids are susceptible to the Rayleigh–Taylor instability. We establish that the problem under consideration is nonlinearly unstable when the surface tension is below the critical value.