Global well-posedness and decay rates for the three dimensional compressible Oldroyd-B model

In this paper, we are concerned with the global well-posedness and decay rates of strong solutions for the three-dimensional compressible Oldroyd-B model. We prove that this set of equations admits a unique global strong solution provided the initial data are close to the constant equilibrium state in H2-framework. Moreover, if the initial data belong to L1, the convergence rate of the solutions in Lp-norm with 2⩽p⩽6 and convergence rates of their spatial derivatives in L2-norm are obtained. It is noteworthy that the smallness restriction on the coupling constant ω is not necessary in this paper.