On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress.This instability is called the Rayleigh-Plateau instabilty.We consider the model developed by Spencer et al.[18],Kirill et al.[10]and Boutat et al.[2]in the case without stress.We obtain a nonlinear parabolic PDE of order four.We show the local existence and uniqueness of the solution of this problem by using Faedo-Galerkin method.The main results are the global existence of the solution and the convergence to the mean value of the initial data for long time.Numerical tests are also presented in this study.