Existence and uniqueness of analytic solution for Rayleigh–Taylor problem

We study the initial value problem for the classical Rayleigh–Taylor problem. If the initial data are analytic in disk containing the unit disk, it is proved that unique solution, which is analytic in for s (1,r), exists locally in time. The analysis is based on a Nirenberg theorem on abstract Cauchy–Kowalewski problem in properly chosen Banach spaces.