Secondary instabilities of linearly heated falling films

O6; Secondary instabilities of linearly heated failing films are studied through three steps. Firstly, the analysis of the primary linear instability on Miladinova's long wave equation of the linearly heated film is performed. Secondly, the similar Landau equation is derived through weak nonlinear theory, and a two-dimensional nonlinear saturation solution of primary instability is obtained within the weak nonlinear domain. Thirdly, the secondary (three-dimensional) instability of the two-dimensional wave is studied by the Floquet theorem.Our secondary instability analysis shows that the Marangoni number has destabilization effect on the secondary instability.