LOW REGULARITY SEMI-LINEAR WAVE EQUATIONS

TERENCE TAO

Abstract. We prove local well-posedness results for the semi-linear wave equation for data in H^{γ}, 0 < γ < \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_{k}^{r,p}.