Year: 2026
Type: preprint
Abstract: In this short note, we prove the global well-posedness of the modified dispersion-generalized Benjamin-Ono equation with dispersion $1<α<2$, $$\partial_t u + D^α\partial_x u + u^2\partial_x u=0,$$ over the Sobolev space $H^s(\mathbb{R})$, 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223409461