Stability of the viscoelastic Rayleigh–Taylor problem with internal surface tension. (December 2020)

• Record Type: Journal Article
• Authors: Zhao, Youyi; Wang, Weiwei; Cao, Junying
• Is Part Of: Nonlinear analysis. Volume 56(2020)
• Publication Date: 2020-12
• Subjects: Rayleigh–Taylor instability -- Stratified viscous fluids -- Incompressible fluids -- Viscoelastic fluids -- Internal surface tension -- Inhibition effect; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103170
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We investigate the stability of the Rayleigh–Taylor (RT) problem for stratified viscoelastic fluids with internal surface tension. More precisely, under the stability condition Dis ( ϑ, κ ) < 1, we prove the existence of unique strong solution with exponential decay in time for the (stratified) viscoelastic RT (VRT) problem with proper initial data in Lagrangian coordinates. This shows that a sufficiently large elasticity coefficient or a sufficiently large surface tension coefficient has a stabilizing effect so that it can inhibit the development of (stratified) RT instability.