Zero diffusion-dispersion limit for the Benjamin–Ono–Burgers equation
Abstract We prove that the solution of the viscous Benjamin–Ono equation converges, as diffusion and dispersion parameters tend to zero (under a suitable balance condition), to the unique entropy solution of the inviscid Burgers equation. The key tool in our proof is Schonbek’s L p -compensated compactness method. Specifically, we prove a uniform L 4 -estimate using a modification of a conserved quantity for the inviscid Benjamin–Ono equation and a suitable differential inequality argument.
Authors
- Eliot Pacherie (ORCID: https://orcid.org/0000-0001-9900-4017)
- Nicola de Nitti
- Giuseppe Maria Coclite (ORCID: https://orcid.org/0000-0001-6019-4757)
- Ola Mæhlen (ORCID: https://orcid.org/0000-0002-1691-9842)
Institutions
- Centre National de la Recherche Scientifique (FR)
- CY Cergy Paris Université (FR)
- Analyse, Géométrie et Modélisation (FR)
Publication Details
- Journal
- Nonlinearity
- Published
- 2025-12-31
- DOI
- https://doi.org/10.1088/1361-6544/ae2227
- Primary Topic
- Advanced Mathematical Physics Problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Universitetet i Oslo
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- Staatssekretariat für Bildung, Forschung und Innovation