On the L² well-posedness and decay estimate of third order Benjamin-Ono equation

2022/08/06 by Wan, Lizhe
#35B65 #35G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.03594

Abstract

We consider the L² 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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