On the initial-boundary value problem of the incompressible viscoelastic fluid system

In this paper, we shall establish the local well‐posedness of the initial‐boundary value problem of the viscoelastic fluid system of the Oldroyd model. We shall also prove that the local solutions can be extended globally and that the global solutions decay exponentially fast as time goes to infinit...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2008-04, Vol.61 (4), p.539-558
Main Authors: Lin, Fanghua, Zhang, Ping
Format: Article
Language:English
Subjects:
Differential equations
Exact sciences and technology
Fluidity
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Viscoelasticity
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Summary:In this paper, we shall establish the local well‐posedness of the initial‐boundary value problem of the viscoelastic fluid system of the Oldroyd model. We shall also prove that the local solutions can be extended globally and that the global solutions decay exponentially fast as time goes to infinity provided that the initial data are sufficiently close to the equilibrium state. © 2007 Wiley Periodicals, Inc.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.20219