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arXiv · 2305.17821

Global solutions of quasi-linear Hamiltonian mKdV equation

Fangchi Yan·Qingtian Zhang
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Abstract

We study the initial value problem of quasi-linear Hamiltonian mKdV equations. Our goal is to prove the global-in-time existence of a solution given sufficiently smooth, localized, and small initial data. To achieve this, we utilize the bootstrap argument, Sobolev energy estimates, and the dispersive estimate. This proof relies on the space-time resonance method, as well as a bilinear estimate developed by Germain, Pusateri, and Rousset.

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Fangchi Yan, Qingtian Zhang. 2023-05-28. Global solutions of quasi-linear Hamiltonian mKdV equation. https://arxiv.org/abs/2305.17821

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