Year: 2026
Type: preprint
Abstract: We consider the good Boussinesq equation on the line. Sufficiently regular solutions are known to converge in the long wave limit to a pair of counterpropagating solutions to the Korteweg--de Vries equation. We prove that this convergence holds for solutions in $H^{-\frac12}$, the largest Sobolev space in which the good Boussinesq equation is well-posed. As part of our analysis, we revisit the well-posedness theory, proving new a priori estimates and a corresponding small data global well-posedness result.
Source: arXiv (Cornell University)
Author: Harrop-Griffiths, Benjamin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223017790