Spectral analysis of the classical Rayleigh-Taylor instability with an upper free surface
In this note, we are interested in the linear Rayleigh-Taylor instability problem for the incompressible fluid with an upper free surface. Using the spectral theory of self-adjoint and compact operator, we rigorously prove the existence of infinitely many normal mode solutions to the linearized equations. Some numerical computations are presented to support our theoretical study.
math.AP↗