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arXiv · 2606.06463

Large data scattering for the defocusing $k$-dispersion generalized Benjamin-Ono equation in the energy space

Luccas Campos·Felipe Linares·Thyago S. R. Santos
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Abstract

We study the defocusing $k$-dispersion generalized Benjamin-Ono equation. For every even integer $k\geq 4$, we prove that solutions with initial data in the energy space $H^{\frac{\alpha}{2}}$ are global in time and scatter. The proof combines the concentration-compactness-rigidity method of Kenig and Merle with techniques based on the Caffarelli-Silvestre extension and Tao's monotonicity formula adapted to the fractional dispersion setting.

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Luccas Campos, Felipe Linares, Thyago S. R. Santos. 2026-06-04. Large data scattering for the defocusing $k$-dispersion generalized Benjamin-Ono equation in the energy space. https://arxiv.org/abs/2606.06463

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