Global solutions to systems of quasilinear wave equations with low regularity data and applications
Global solutions to systems of quasilinear wave equations with low regularity data and applications
复制标题
DOI：
10.1016/j.matpur.2020.05.006
复制
发表时间：
2020-05
期刊：
影响因子：
--
通讯作者：
Dongbing Zha;K. Hidano
中科院分区：
文献类型：
--
作者：
Dongbing Zha;K. Hidano
本文研究了具有低正则性初始数据的满足零条件的三维拟线性波动方程系统的Cauchy问题。在径向对称情况下，我们证明了H 3× H 2中每一个小数据的全局存在性。为了实现这一目标，我们将展示如何将Li和Chen(1988)[32]首次提出的全局迭代方法扩展到低正则性情况，这也是本文的另一个目的。最后，将所得结果应用于三维非线性弹性波。
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× 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.