Global existence of solutions for the second grade fluid equations in a thin three-dimensional domain

Article type: Research Article

Authors: Abdelhedi, Bouthaina

Affiliations: Département de Mathématiques, Faculté des Sciences, Université de Sfax, BP 1171, Route Soukra km 3.5, 3000 Sfax, Tunisia. E-mail: bouthaina_abde@yahoo.fr

Abstract: We consider the second grade fluid equations on a thin three-dimensional domain with periodic boundary conditions. We prove global existence and uniqueness of the solution for large initial data. We use an appropriate decomposition of solution u into a v part, which is solution of a 2D second grade fluid equations and the remaining w part which has an initial data converging to 0 as the thickness of the thin domain goes to 0.

Keywords: Second grade fluid equations, thin domains, perturbation, global existence

DOI: 10.3233/ASY-161397

Journal: Asymptotic Analysis, vol. 101, no. 1-2, pp. 69-95, 2017