ON THE CAUCHY PROBLEM FOR A COMPRESSIBLE OLDROYD-B MODEL WITHOUT STRESS DIFFUSION

This article is devoted to the global well-posedness and associated time-decay estimates of strong solutions for the compressible Oldroyd-B model without stress diffusion in R-3. By introducing a new linearized system and analyzing its time decay in the low-frequency regime, we establish the uniform estimates of the corresponding nonlinear system. The global-in-time well-posedness is then established near an equilibrium state by the standard continuity method. This work can be viewed as an extension of W. Wang and H. Wen [Math. Models Methods Appl. Sci., 30 (2020), pp. 139-179], where the stress diffusion is included.