On the stability of Rayleigh–Taylor problem for stratified rotating viscoelastic fluids

Abstract

We investigate the stability of Rayleigh-Taylor (RT) problem of the stratified incompressible viscoelastic fluids under the rotation and the gravity in a horizontal periodic domain, in which the rotation axis is parallel to the direction of gravity, the two fluids are immiscible, and the heavier fluid lies on the lighter one. We establish a stability condition for the RT problem. Moreover, we prove that, under the stability condition, the RT problem enjoys a unique strong solution, which exponentially decays with respect to time. In addition, we note that the stability condition is independent of rotation angular velocity, and the rotation has no destabilizing effect.

On classical solutions of Rayleigh–Taylor instability in inhomogeneous viscoelastic fluids

“…The RT instability in viscoelastic fluid has been widely studied, see [15,25,27] for examples. Moreover, the RT instability also has been investigated under other physical factors, such as internal surface tension [12,17,41], magnetic fields [4, 5, 19-21, 23, 24, 39, 40], rotation [3,6,29], and so on. We also refer to [2,8,14,30,[33][34][35][36] for related progress in other mathematical problems of hydromechanics.…”