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

2024/10/17 by Li Tu, Yi Zhou, Tu, Li +1 · 1 citation
Mathematics · Physics and Astronomy · #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2410.13656

openalex publication_date 2024/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^(1)/(4)(ℝ) and H^(1)/(2)(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.

Cited by

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

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