The paper is devoted to asymptotic behavior for a compressible Oldroyd-B model in \(\mathbb{T}^{2}\). We prove that the weak solution will converge to the strong solution as the rough initial data of the former tend to the smooth initial data of the latter. The proof relies on a relative entropy method. This work can be viewed as a generalization of the weak-strong uniqueness where the initial data for the weak solution and the strong solution are smooth and the same. The main challenges focus on a \(L^{2}\)-type estimate for the extra stress tensor difference \(\tau^{\theta}-\tau^{*}\) due to the absence of \(L^{2}\)-norm of \(\tau^{\theta}\) in the entropy estimate and that the initial data of the weak solution are rough here. To handle these, some commutator estimates are adopted.

本文致力于\（\ mathbb {T} ^ {2} \）中可压缩Oldroyd-B模型的渐近行为。我们证明了弱解将收敛于强解，因为前者的粗略初始数据趋向于后者的平滑初始数据。证明依赖于相对熵方法。可以将这项工作视为弱强唯一性的概括，其中弱解和强解的初始数据是平滑且相同的。主要挑战集中在由于缺少\（L ）的额外应力张量差\（\ tau ^ {\ theta}-\ tau ^ {*} \）的\（L ^ {2} \）型估计上。^ {2} \） - \（\ tau ^ {\ theta} \）的范数在熵估计中，弱解的初始数据在这里是粗糙的。为了解决这些问题，采用了一些换向器估计。