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

• Main Authors: Yuping Chen, Weiwei Wang, Youyi Zhao
• Format: Article
• Language: English
• Published: SpringerOpen 2018-08-01
• Series: Journal of Inequalities and Applications
• Subjects: Stratified viscoelastic fluids; Rayleigh–Taylor instability; Stratified magnetohydrodynamic fluids
• Online Access: http://link.springer.com/article/10.1186/s13660-018-1796-6

Abstract It is well known that there exists a threshold κc $\kappa_{{c}}$ such that the linearized stratified viscoelastic Rayleigh–Taylor problem is unstable for the elasticity coefficient κ satisfying κ<κc $\kappa <\kappa_{{c}}$. In this paper, we further prove that if κ<κc $\kappa <\kappa_{{c}}$, 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 κc $\kappa_{{c}}$. In addition, we further extend the obtained results in the linearized stratified viscoelastic Rayleigh–Taylor problem to the linearized stratified magnetic Rayleigh–Taylor problem.