Asymptotic profiles for the third grade fluids equations. (May 2015)

• Record Type: Journal Article
• Authors: Coulaud, Olivier
• Is Part Of: International journal of non-linear mechanics. Volume 71(2015)
• Page Start: 132
• Page End: 151
• Publication Date: 2015-05
• Subjects: Fluid mechanics -- Third grade fluids -- Asymptotic expansion; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2014.11.018
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: We study the long time behaviour of the solutions of the third grade fluids equations in dimension 2. Introducing scaled variables and performing several energy estimates in weighted Sobolev spaces, we describe the first order of an asymptotic expansion of these solutions. It shows in particular that, under smallness assumptions on the data, the solutions of the third grade fluids equations converge to self-similar solutions of the heat equations, which can be computed explicitly from the data.