Low Regularity Semi-Linear Wave Equations
Terence Tao
We prove local well-posedness results for the semi-linear wave equation for data in $H^\gamma, 0 < \gamma < \frac{n-3}{2(n-1)}$, extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space $X^{r,p}_{k}$.