论文标题
在弱零半线性方程的系统上
On a System of Weakly Null Semilinear Equations
论文作者
论文摘要
我们开发了一种新方法来解决某些弱空的波动方程系统。这种方法不依赖洛伦兹的不变性，也不依赖于零叶的使用，这两者都将应用程序限制为例如多速度系统。该证明使用了第一作者Tataru和Tohaneanu的一类时空Klainerman-Sobolev估计值，它们与当地能量估计很好地搭配了Dafermos和Rodnianski的$ r^{p} $加权方法与Alinhac的幽灵权重方法。我们通过修改$ \ partial_ {t} - \ partial_ {r} $部分乘以乘数的$ \ partial_ {t} - 部分。
We develop a new method for addressing certain weakly null systems of wave equations. This approach does not rely on Lorentz invariance nor on the use of null foliations, both of which restrict applications to, e.g., multiple speed systems. The proof uses a class of space-time Klainerman-Sobolev estimates of the first author, Tataru, and Tohaneanu, which pair nicely with local energy estimates that combine the $r^{p}$-weighted method of Dafermos and Rodnianski with the ghost weight method of Alinhac. We further refine the standard local energy estimate with a modification of the $\partial_{t} - \partial_{r}$ portion of the multiplier.
