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arXiv · 2407.01472

The dispersion generalized Benjamin-Ono equation

Albert Ai·Grace Liu
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Abstract

We consider the well-posedness of the family of dispersion generalized Benjamin-Ono equations. Earlier work of Herr-Ionescu-Kenig-Koch established well-posedness with data in $L^2$, by using a discretized gauge transform in the setting of Bourgain spaces. In this article, we remain in the simpler functional setting of Sobolev spaces, and instead combine a pseudodifferential gauge transform, a paradifferential normal form, and a variable coefficient Strichartz analysis to establish well-posedness in negative-exponent Sobolev spaces. Our result coincides with the classical well-posedness results obtained at the Benjamin-Ono and KdV endpoints.

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Albert Ai, Grace Liu. 2024-07-01. The dispersion generalized Benjamin-Ono equation. https://arxiv.org/abs/2407.01472

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