Rayleigh-Taylor instability for nonhomogeneous incompressible fluids with Navier-slip boundary conditions
- Resource Type
- Working Paper
- Authors
- Ding, Shijin; Ji, Zhijun; Li, Quanrong
- Source
- Subject
- Mathematics - Analysis of PDEs
- Language
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.
Comment: 30 pages