Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations (II)

We study the Zakharov system in two and three spatial dimensions, reproducing the optimal local well-posedness results from Bejenaru-Herr-Holmer-Tataru [2] and Bejenaru-Herr [1]. The main tools are similar to [16], based on a bilinear estimate, which is proved in a physical space approach by a new type of div-curl lemma. The new ingredient of our proof is a Strichartz estimate with mixed spatial integrability.