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arXiv · 2608.10767

Decay and regularity properties for the dispersion generalized Benjamin-Ono equation

Germán Fonseca·Oscar Riaño·Guillermo Rodríguez-Blanco
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Abstract

We study spatial decay properties of solutions to the dispersion generalized Benjamin-Ono equation. We first establish persistence properties in weighted Sobolev spaces under a sharp condition between decay and regularity, improving previous results. Additionally, extending recent works on the Benjamin-Ono equation by Linares and Ponce [27], we also show that decay at two distinct times implies additional regularity of solutions. The proof relies on weighted energy estimates and pseudo-differential methods, which build on an iterative mechanism that trades decay for regularity.

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Germán Fonseca, Oscar Riaño, Guillermo Rodríguez-Blanco. 2026-08-11. Decay and regularity properties for the dispersion generalized Benjamin-Ono equation. https://arxiv.org/abs/2608.10767

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