The Cauchy problem for an Oldroyd-B model in three dimensions

作者：Wang, Wenjun; Wen, Huanyao^*

来源：Mathematical Models and Methods in Applied Sciences, 2020, 30(1): 139-179.

DOI：10.1142/S0218202520500049

• Compressible Oldroyd-B model
• global well posedness
• time-decay rates

We consider an Oldroyd-B model which is derived in Ref. 4 [J. W. Barrett, Y. Lu and E. Suli, 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 eta, in the equation for the extra stress tensor and in the momentum equation, lead to new technical difficulties, such as deducing (LtLx2)-L-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.