On effects of elasticity and magnetic fields in the linear Rayleigh–Taylor instability of stratified fluids

It is well known that there exists a threshold [Formula: see text] such that the linearized stratified viscoelastic Rayleigh–Taylor problem is unstable for the elasticity coefficient κ satisfying [Formula: see text] . In this paper, we further prove that if [Formula: see text] , then there exists an unstable solution to the linearized stratified viscoelastic Rayleigh–Taylor problem with a largest growth rate. Moreover, the largest growth rate decreases from a positive constant to 0 as κ increases from 0 to [Formula: see text] . In addition, we further extend the obtained results in the linearized stratified viscoelastic Rayleigh–Taylor problem to the linearized stratified magnetic Rayleigh–Taylor problem.