Stability of the viscoelastic Rayleigh–Taylor problem with internal surface tension. (December 2020) - Zhao, Youyi; Wang, Weiwei; Cao, Junying
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.