Global existence of the 3D rotating second grade fluid system

Article type: Research Article

Authors: Jaffal-Mourtada, Basma^{; *}

Affiliations: Léonard de Vinci Pôle Universitaire, Research Center, 92 916 Paris La Défense, France. E-mail: basma.jaffal@devinci.fr

Correspondence: [*] Corresponding author. E-mail: basma.jaffal@devinci.fr.

Abstract: We consider the equations of a rotating incompressible non-Newtonian fluid flow of grade two in a three dimensional torus. We prove two different results of global existence of strong solutions. In the first case, we consider that the elasticity coefficient α is arbitrary and we suppose that the third components of the vertical average of the initial data and of the forcing term are small compared to the horizontal components. In the second case, we consider a forcing term and initial data of arbitrary size but we restrict the size of α. In both cases, we show that the limit system is composed of a linear system and a second grade fluid system with two variables and three components.

Keywords: Non-newtonian fluid, second grade fluid, global existence, rotating fluid, limit system

DOI: 10.3233/ASY-201644

Journal: Asymptotic Analysis, vol. 124, no. 3-4, pp. 259-290, 2021