Kavli Affiliate: Yi Zhou
| First 5 Authors: Xinfeng Hu, Xinfeng Hu, , ,
| Summary:
The work by Kenig-Ponce-Vega [15] initiated the use of Bourgain spaces to
study the low-regularity well-posedness of semilinear dispersive equations.
Since then, the Bourgain space method has become the dominant, and almost the
only method to deal with this problem. The goal of this series of papers is to
propose an alternative approach for this problem that does not rely on Bourgain
spaces. Our method is based on a bilinear estimate, which is proved in a
physical space approach by a new div-curl type lemma introduced by the third
author. Combining these ingredients with a Strichartz estimate of mixed spatial
integrability, we will illustrate our method in the present paper by
reproducing best known local well-posedness results for the 2d and 3d Zakharov
system from Bejenaru-Herr-Holmer-Tataru [2] and Bejenaru-Herr [1].
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