On nonlinear Rayleigh-Taylor instabilities (Q2508623)

The authors study the stability of interface between two incompressible inviscid immiscible fluids with different densities in the presence of a constant gravity field. The linearly unstable modes for Rayleigh-Taylor instability are shown to become nonlinearly unstable for the full nonlinear system, with explicit growth estimates. The proof is based on the abstract Cauchy-Kovalevskaya theorem applied to Fourier-transformed equations in analytic spaces.