Global wellposedness and large time behavior of solutions to the N-dimensional compressible Oldroyd-B model

The purpose of this paper is to study the global wellposedness and large time behavior results strong solutions for compressible Oldroyd-B model derived by Barrett, Lu, Süli (Commun. Math. Sci., 15, 1265–1323, 2017). Exploiting harmonic analysis tools (especially Littlewood-Paley theory), we first well-posedness with small initial data in spaces low regularity. Then, under some suitable conditions involving only frequency data, also obtain optimal decay rates solutions. Compared result Wang Wen (Math. Models Methods Appl. 30, 139–179, 2020), polymer number density allowed vanish stress tensor near zero equilibrium.