The Rayleigh-Taylor instability of incompressible Euler equations in a horizontal slab domain

Abstract

In this paper, we consider the Rayleigh-Taylor instability of incompressible Euler equations in a horizontal slab domain, which develops the results of Hwang and Guo (2003) in [11] by taking into account the boundary condition. If a steady density profile is non-monotonic, then the smooth steady state is nonlinearly unstable. Moreover, we also give a new proof for the local existence to inhomogeneous incompressible Euler equations in a smooth bounded domain Ω⊂Rn, with initial data in Hs(Ω)(s>n2+1).