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arXiv · 2208.03594

On the $L^2$ well-posedness and decay estimate of third order Benjamin-Ono equation

Lizhe Wan
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Abstract

We consider the $L^2$ well-posedness of third order Benjamin-Ono equation. We show that by means of a normal form and a gauge transformation, the equation can be changed into an Airy-type equation. A second goal of this work is to establish that the solutions to the nonlinear third order Benjamin-Ono equation problem exhibit a dispersive decay estimate analogue to the corresponding linear associated problem. The key ingredient is the use of a nonlinear vector field method.

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Lizhe Wan. 2022-08-06. On the $L^2$ well-posedness and decay estimate of third order Benjamin-Ono equation. https://arxiv.org/abs/2208.03594

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