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Global well-posedness for the modified dispersion-generalized Benjamin-Ono equations
Abstract
In this short note, we prove the global well-posedness of the modified dispersion-generalized Benjamin-Ono equation with dispersion 1<α<2, ∂t u + Dα∂x u + u2∂x u=0, over the Sobolev space Hs(ℝ), for any regularity s greater or equal than the sharp analytic well-posedness regularity. As a byproduct, we also derive nonlinear smoothing estimates and give a simple proof of local well-posedness.
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BibTeX
@misc{baldasso2026global,
title = {{Global well-posedness for the modified dispersion-generalized Benjamin-Ono equations}},
author = {Mikaela Baldasso and Simão Correia and Thyago S. R. Santos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30275},
eprint = {2610.30275},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30275},
}
RIS
TY - UNPB
TI - Global well-posedness for the modified dispersion-generalized Benjamin-Ono equations
AU - Mikaela Baldasso
AU - Simão Correia
AU - Thyago S. R. Santos
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30275
UR - https://arxiv.org/abs/2610.30275
AB - In this short note, we prove the global well-posedness of the modified dispersion-generalized Benjamin-Ono equation with dispersion 1<α<2, ∂_t u + D^α∂_x u + u^2∂_x u=0, over the Sobolev space H^s(ℝ), for any regularity s greater or equal than the sharp analytic well-posedness regularity. As a byproduct, we also derive nonlinear smoothing estimates and give a simple proof of local well-posedness.
ER -