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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
classification math.AP
keywords proofbilinearequationsestimatefracmathbbmodifiedapplications
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations

    math.AP 2026-08 conditional novelty 7.0 of 10

    Free Dirac solutions have a one-dimensional div-curl structure that yields frequency-localized L2 bilinear null-form estimates, with an additional K/m gain for low-frequency same-branch pseudoscalar interactions.

  2. Global well-posedness in the critical Besov space of the skew mean curvature flow in $\mathbb{R}^d: d\ge 5$

    math.AP 2025-05 conditional novelty 7.0 of 10

    Global well-posedness at critical Besov regularity B^{d/2-1}_{2,1} for the skew mean curvature flow in R^d, d >= 5, with small initial data.

  3. 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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