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.

中文翻译：

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具有Navier滑移边界条件的非均匀不可压缩流体的Rayleigh-Taylor不稳定性

本文涉及无限平板中稳态附近具有Navier滑移边界条件的非均匀不可压缩Navier-Stokes方程的Rayleigh-Taylor不稳定性，其中Navier-滑移系数没有定义符号，并且平板在水平方向上是周期性的。江等人的动机。（Sci。China Math。，2013），我们将结果从Dirichlet边界条件扩展到Navier-slip边界条件。我们的结果表明，“随着高度增加，密度增加”仍在Navier滑移边界条件下的不稳定性中起着关键作用。