In this paper, we study the Cauchy problem for systems of 3-D quasilinear wave equations satisfying the null condition with initial data of low regularity. In the radially symmetric case, we prove the global existence for every small data in $H^3\times H^2$ with a low weight. To achieve this goal, we will show how to extend the global iteration method first suggested by Li and Chen (1988) [32] to the low regularity case, which is also another purpose of this paper. Finally, we apply our result to 3-D nonlinear elastic waves.

中文翻译：

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具有低规则性数据的拟线性波动方程系统的整体解及其应用

在本文中，我们研究了满足零条件且初始数据具有低规则性的3-D拟线性波动方程组的柯西问题。在径向对称的情况下，我们证明了每个小数据的全局存在$H^3\times H^2$重量轻。为了实现这个目标，我们将展示如何将由Li和Chen（1988）[32]首次提出的全局迭代方法扩展到低规则性情况，这也是本文的另一个目的。最后，我们将结果应用于3D非线性弹性波。