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

Li Tu; Yi Zhou

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arXiv · 2410.13656

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

Li Tu·Yi Zhou

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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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Li Tu, Yi Zhou. 2024-10-17. Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations. https://arxiv.org/abs/2410.13656

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