论文标题
验证方程满足无效条件的全球存在
Global existence for quasilinear wave equations satisfying the null condition
论文作者
论文摘要
当初始数据足够小时，我们探讨了对质波方程系统满足无效条件的全局解决方案的全球存在。我们适应了Keel，Smith和Sogge的一种方法，该方法依赖于本地能源估计值和加权Sobolev估算值，该估算通过使用$ r^p $加权的dafermos和Rodnianski的本地能量估计来产生$ | x | $的衰减。这种方法的一个优点是，可以避免所有与时间有关的向量场，并且可以轻松地适应证明以解决波动方程与星形障碍物的外观。
We explore the global existence of solutions to systems of quasilinear wave equations satisfying the null condition when the initial data are sufficiently small. We adapt an approach of Keel, Smith, and Sogge, which relies on integrated local energy estimates and a weighted Sobolev estimate that yields decay in $|x|$, by using the $r^p$-weighted local energy estimates of Dafermos and Rodnianski. One advantage of this approach is that all time-dependent vector fields can be avoided and the proof can be readily adapted to address wave equations exterior to star-shaped obstacles.
