Stability and Exponential Decay for the Compressible Oldroyd‐B Model Without Stress Diffusion

ABSTRACT In this paper, we establish the global stability and large time behavior of strong solutions to the compressible Oldroyd‐B model without stress diffusion in . In addition, the ‐norm of the solutions is shown to be stable and decay exponentially in time by a bootstrap argument. In particular, we extend Liu‐Lu‐Wen's result (SIAM J. Math. Anal., 53 (2021), 6216–6242) to the bounded domains, where they consider the Cauchy problem and obtain the algebraic decay behavior of strong solution.