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

Published 2 Jul 2025 in math.AP | (2507.01317v1)

Abstract: 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.

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