Existence and stability of the steady state solution of a thin film on an inclined periodic solid substrate under gravity

Article type: Research Article

Authors: Alhasanat, Ahmad | Ou, Chunhua^{; *}

Affiliations: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada, A1C 5S7. E-mails: A.Alhasanat@mun.ca, ou@mun.ca

Correspondence: [*] Corresponding author. E-mail: ou@mun.ca.

Abstract: In this paper, we investigate the dynamics of a liquid film flowing over a periodic wavy wall. This study is based on a long-wave model that is valid at near-critical Reynolds number. For the periodic wall surface, we prove the existence of a periodic steady-state solution to the model by the method of abstract contraction mapping in a particular functional space. Using the Floquet–Bloch theory and asymptotic method, we establish several analytic results on the stability of the periodic steady-state solution in a weighted functional space.

Keywords: Thin film flow, periodic solution, asymptotic analysis

DOI: 10.3233/ASY-171431

Journal: Asymptotic Analysis, vol. 104, no. 3-4, pp. 191-207, 2017