Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces

Simão Correia

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arXiv · 2008.05508

Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces

Simão Correia

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Abstract

We consider the Benjamin-Ono equation on the real line for initial data in weighted Sobolev spaces. After the application of the gauge transform, the flow is shown to be Lipschitz continuous and to present a nonlinear smoothing effect. As a consequence, unconditional uniqueness for the Benjamin-Ono equation is proved.

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Simão Correia. 2020-08-12. Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces. https://arxiv.org/abs/2008.05508

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