Low Regularity Semi-linear Wave Equations

  title={Low Regularity Semi-linear Wave Equations},
  author={Terence Tao},
We prove local well-posedness results for the semi-linear wave equation for data in H γ , 0 < γ < 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 .