On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion

In this paper, we are concerned with the Cauchy problem of the compressible Oldroyd-B model without stress diffusion in Rn(n=2,3). The absence of stress diffusion introduces significant challenges in the analysis of this system. By employing tools from harmonic analysis, particularly the Littlewood–Paley decomposition theory, we establish the global well-posedness of solutions with initial data in Lp critical spaces, which accommodates the case of large, highly oscillating initial velocity. Furthermore, we derive the optimal time decay rates of the solutions by a suitable energy argument.