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 $$ such that the linearized stratified viscoelastic Rayleigh-Taylor problem is unstable for the elasticity coefficient κ satisfying $$ . In this paper, we further prove that if $$ , then there exists an unstable solution to the linearized stratified viscoelastic Rayleigh-Taylor problem with a largest growth rate. Moreover, the largest growth rate decreases from a positive constant to 0 as κ increases from 0 to $$ . In addition, we further extend the obtained results in the linearized stratified viscoelastic Rayleigh-Taylor problem to the linearized stratified magnetic Rayleigh-Taylor problem.