On the dynamical Rayleigh-Taylor instability (Q1416766)

The authors consider density-dependent Euler equations for an incompressible fluid. Exponentially growing solutions exist for the linearized perturbation equations. The main purpose of the current work is to demonstrate the Rayleigh-Taylor instability for the fully nonlinear dynamical setting. The main difficulties in such a setting are the presence of the continuum spectrum, as well as the unbounded higher-order terms. In the dynamic instability for certain physical systems, the sharp exponential growth rate is controlled by a dominating eigenvalue of the corresponding linearized system. The authors find the dominant eigenvalues by using variational methods, and combine the approximate solution with the classical energy estimate, to derive the nonlinear instability.