Communications in Mathematical Sciences
Volume 14 (2016)
An improved result on Rayleigh–Taylor instability of nonhomogeneous incompressible viscous flows
Pages: 1269 – 1281
In [F. Jiang and S. Jiang, Adv. Math., 264, 831–863, 2014], the author and Jiang investigated the instability of Rayleigh–Taylor steady-state of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain $\Omega$ of class $C^2$. In particular, we proved the steady-state is nonlinearly unstable under a restrictive condition of that the derivative function of steady density possesses a positive lower bound. In this article, by exploiting a standard energy functional and more-refined analysis of error estimates in the bootstrap argument, we further show the nonlinear instability result without the restrictive condition.
Navier–Stokes equations, steady state solutions, Rayleigh–Taylor instability
2010 Mathematics Subject Classification