Abstract This paper is concerned with the global well-posedness issue of the compressible viscoelastic fluids in the whole space R N , N ≥ 2 . The proof relies on the dispersive estimates to the linearized hyperbolic system combined with energy estimates to the hyperbolic-parabolic system. By exploiting the intrinsic structure of the system under some physical restrictions, we find that the compressible viscoelastic fluids admits a unique global solution with a class of large initial data in the sense of critical L 2 framework.

中文翻译：

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可压缩粘弹性流体的色散效应和全局适定性

摘要 本文研究了整个空间RN , N ≥ 2 中可压缩粘弹性流体的全局适定性问题。证明依赖于对线性化双曲线系统的色散估计以及对双曲-抛物线系统的能量估计。通过在某些物理限制下利用系统的内在结构，我们发现可压缩粘弹性流体在临界 L 2 框架意义上承认具有一类大初始数据的独特全局解。