On the dynamic instability of non‐Newtonian fluids driven by gravity

Abstract

In this paper, we investigate the instability for Rayleigh–Taylor problem of three‐dimensional incompressible non‐Newtonian fluids with Eills‐type. If the density profile in equilibrium‐state is heavier with increasing height, we prove that the equilibrium‐state solution is unstable under ‐norm by exploiting a bootstrap method.