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

Li Tu; Yi Zhou

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

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arxiv 2410.13656 v2 pith:TOH5ET6V submitted 2024-10-17 math.AP

Li Tu , Yi Zhou This is my paper · ORCID

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abstract

We give a simpler proof for the local well-posedness of the modified Korteweg-de Vries equations and modified Benjamin-Ono equation in $H^{\frac{1}{4}}(\mathbb{R})$ and $H^{\frac{1}{2}}(\mathbb{R})$, respectively. The proof is based on the Strichartz estimate, dyadic decomposition and a bilinear estimate given by a new type of div-curl lemma.

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Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations (II)
math.AP 2025-07 conditional novelty 5.0 of 10

A physical-space bilinear estimate method reproduces the sharpest known local well-posedness thresholds for the 2d and 3d Zakharov system without Bourgain spaces.

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