Study of generalized Stokes operator in a thin domain with friction law (case p < 2). (2nd April 2018)

• Record Type: Journal Article
• Authors: Dilmi, Mohamed; Dilmi, Mourad; Benseridi, Hamid
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 9027
• Page End: 9036
• Publication Date: 2018-04-02
• Subjects: a priori estimates -- Reynolds equation -- Stokes systems -- Tresca law -- variational formulation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4876
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this work, we consider a mathematical model of an incompressible fluid governed by the generalized Stokes system in a stationary regime in a 3‐dimensional thin domain Ω ϵ with Tresca friction law. The problem statement and variational formulation of the problem are formulated. Then the estimates on velocity and pressure are proved in a fixed domain. Finally, our main goal concerns the specific Reynolds equation and the uniqueness of the solution û ϵ, π ^ ϵ are obtained.