Communications in Mathematical Sciences
Volume 15 (2017)
Global existence for viscoelastic fluids with infinite Weissenberg number
Pages: 1129 – 1140
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.
viscoelastic fluids, global existence, Kawashima condition, compatibility conditions
2010 Mathematics Subject Classification
35A01, 35Q35, 76A10