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. The Oldroyd-B model is a typical class of viscoelastic fluids. There are some studies about the solution and rates about incompressible Oldroyd-B model and 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.lt is noteworthy that the smallness restriction on the coupling constant ? is not necessary in this paper.