In this paper, we are concerned with the global well-posedness and decay rates of strong solutions for the three-dimensional compressible Phan-Thein–Tanner 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 \(H^3\)-framework. Moreover, if the initial data belong to \(L^{1}\), the convergence rates of the higher-order spatial derivatives of the solution are obtained by combining the decay estimates for the linearized equations and the Fourier splitting method.

中文翻译：

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三维可压缩 Phan-Thein-Tanner 模型的整体适中性和衰减率

在本文中，我们关注三维可压缩 Phan-Thein-Tanner 模型强解的全局适定性和衰减率。我们证明，如果初始数据接近\(H^3\)框架中的恒定平衡状态，则这组方程允许唯一的全局强解。此外，如果初始数据属于\(L^{1}\)，则通过结合线性化方程的衰减估计和傅立叶分裂方法，可以获得解的高阶空间导数的收敛速度。