Rayleigh-Taylor instability for nonhomogeneous incompressible fluids with Navier-slip boundary conditions

摘要

This paper is concerned with the Rayleigh-Taylor instability for the nonhomogeneous incompressible Navier-Stokes equations with Navier-slip boundary conditions around a steady state in an infinite slab, where the Navier-slip coefficients do not have defined sign and the slab is horizontally periodic. Motivated by Jiang et al. (Sci. China Math., 2013), we extend the result from Dirichlet boundary condition to Navier-slip boundary conditions. Our results indicate the factor that "heavier density with increasing height" still plays a key role in the instability under Navier-slip boundary conditions.