The globally exponential decay and inviscid limit of analytic solutions to the compressible Oldroyd-B model

In this paper, we derive the globally exponential decay and inviscid limit of analytic solutions to the compressible Oldroyd-B model. Due to the pure damping effects of the linearized compressible Oldroyd-B model without viscosity, we obtain a globally viscosity-independent a priori estimate. However, the bilinear term possesses one more order of derivative than the linear part, and no effective structure has been found to address this derivative loss problem. Therefore, we can only establish our results in the analytic energy space rather than the Sobolev space.