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

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.

The current version will undergo substantial revisions, including significant changes to the manuscript and authorship. We therefore withdraw this version and plan to submit a substantially revised version in the future