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).
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