In this paper, we show the global existence of classical solutions to the incompressible elastodynamics equations with a damping mechanism on the stress tensor in dimension three for sufficiently small initial data on periodic boxes, that is, with periodic boundary conditions. The approach is based on a time-weighted energy estimate, under the assumptions that the initial deformation tensor is a small perturbation around an equilibrium state and the initial data have some symmetry.

中文翻译：

---

带阻尼弹性动力学方程的整体经典解

在本文中，对于周期盒上足够小的初始数据，我们显示了在维数为3的应力张量上具有阻尼机制的不可压缩弹性动力学方程经典解的整体存在性。该方法基于时间加权能量估计，并假设初始变形张量是围绕平衡状态的小扰动，并且初始数据具有一定的对称性。