Communications in Mathematical Sciences

Volume 15 (2017)

Number 4

Global existence for viscoelastic fluids with infinite Weissenberg number

Pages: 1129 – 1140

DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n4.a10

Authors

Xiaokai Huo (Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China)

Wen-An Yong (Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China)

Abstract

In this article, we show that the recently studied compressible and incompressible models for viscoelastic fluids with infiniteWeissenberg number can be well regarded as specific examples of general hyperbolic-parabolic systems studied by Shizuta and Kawashima. It will be seen that two physically motivated compatibility conditions compensate the breaking of the Kawashima condition. Thus, the global existences of classical small solutions near equilibrium can be easily proved by following the general framework.

Keywords

viscoelastic fluids, global existence, Kawashima condition, compatibility conditions

2010 Mathematics Subject Classification

35A01, 35Q35, 76A10

Published 16 May 2017