Global well-posedness for the Benjamin equation in low regularity

Yongsheng Li; Yifei Wu

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arXiv · 0910.4533

Global well-posedness for the Benjamin equation in low regularity

Yongsheng Li·Yifei Wu

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Abstract

In this paper we consider the initial value problem of the Benjamin equation $$ \partial_{t}u+ν\H(\partial^2_xu) +μ\partial_{x}^{3}u+\partial_xu^2=0, $$ where $u:\R\times [0,T]\mapsto \R$, and the constants $ν,μ\in \R,μ\neq0$. We use the I-method to show that it is globally well-posed in Sobolev spaces $H^s(\R)$ for $s>-3/4$. Moreover, we use some argument to obtain a good estimative for the lifetime of the local solution, and employ some multiplier decomposition argument to construct the almost conserved quantities.

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Yongsheng Li, Yifei Wu. 2009-10-23. Global well-posedness for the Benjamin equation in low regularity. https://arxiv.org/abs/0910.4533

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