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arXiv · 2003.10665

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

Shijin Ding·Zhijun Ji·Quanrong Li
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Abstract

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 [18], 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.

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Shijin Ding, Zhijun Ji, Quanrong Li. 2020-03-24. Rayleigh-Taylor instability for nonhomogeneous incompressible fluids with Navier-slip boundary conditions. https://doi.org/10.1002/mma.6376

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