Approximation of a Class of Incompressible Third Grade Fluids Equations. (31st March 2015)

• Record Type: Journal Article
• Authors: Zhu, Zeqi; Li, Hongxia; Fu, Jianjun; Sheng, Qian
• Other Names: Area Ivan Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-03-31
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/627584
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : This paper discusses the approximation of weak solutions for a class of incompressible third grade fluids equations. We first introduce a family of perturbed slightly compressible third grade fluids equations (depending on a positive parameterϵ ) which approximate the incompressible equations asϵ → 0 + . Then we prove the existence and uniqueness of weak solutions for the slightly compressible equations and establish that the solutions of the slightly compressible equations converge to the solutions of the incompressible equations.