Further existence results for classical solutions of the equations of a second-grade fluid
type: Item
instance of: scholarly article
title: Further existence results for classical solutions of the equations of a second-grade fluid
zbMATH Open document ID: 0833.76005
DOI: 10.1007/BF00387710
author: Adélia Sequeira
author: Giovanni Paolo Galdi
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-02-15T00:00:00Z
review text: A theoretical investigation is carried out on the equations of motion of an incompressible homogeneous fluid of the second grade. The question of existence and uniqueness of solution is revisited with the objective of removing a restriction on a material parameter \(\alpha =1/\rho \) imposed in previous works. By an appropriate splitting of the original problem along with the use of Schauder fixed point theorem, the authors show that if the domain \(\Omega\) is simply connected and the initial data not too large, the problem admits a unique classical solution, global in time, for any \(\alpha>0\). This is an interesting result in the area of theoretical non-Newtonian fluid mechanics, and it is presented in a very well-written paper.
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 754028
zbMATH Keywords: global in time classical solution
zbMATH Keywords: incompressible homogeneous fluid
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: material parameter
zbMATH Keywords: splitting
zbMATH Keywords: Schauder fixed point theorem
reviewed by: H. Ramkissoon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 754028