Nonlinear Rayleigh-Taylor instability for the two-phase Euler equations with surface tension

We consider the free boundary problem for two layers of immiscible, inviscid, incompressible fluid in a uniform gravitational field. The surface tension at the free interface between the two fluids is included so as to exclude the Kelvin-Helmholtz instability, while the upper fluid is assumed to be heavier than the lower fluid so that the fluids are susceptible to the Rayleigh-Taylor instability. We establish that the problem under consideration is nonlinearly unstable when the surface tension is below the critical value. (C) 2019 Elsevier Ltd. All rights reserved.