1. The Cauchy problem for an Oldroyd-B model in three dimensions.
- Author
-
Wang, Wenjun and Wen, Huanyao
- Subjects
CAUCHY problem ,SOBOLEV spaces ,NAVIER-Stokes equations ,DIMENSIONS ,MATHEMATICS ,EQUATIONS - Abstract
We consider an Oldroyd-B model which is derived in Ref. 4 [J. W. Barrett, Y. Lu and E. Süli, Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model, Commun. Math. Sci.15 (2017) 1265–1323] via micro–macro-analysis of the compressible Navier–Stokes–Fokker–Planck system. The global well posedness of strong solutions as well as the associated time-decay estimates in Sobolev spaces for the Cauchy problem are established near an equilibrium state. The terms related to η , in the equation for the extra stress tensor and in the momentum equation, lead to new technical difficulties, such as deducing L t 2 L x 2 -norm dissipative estimates for the polymer number density and its spatial derivatives. One of the main objectives of this paper is to develop a way to capture these dissipative estimates via a low–medium–high-frequency decomposition. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF