Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems

Ver/Abrir
Identificadores
URI: https://hdl.handle.net/10902/29575
ISSN: 0026-9255
ISSN: 1436-5081
Compartir
Estadísticas
Ver Estadísticas
Google Scholar
Registro completo
Mostrar el registro completo DC
Autoría
Bae, Hantaek; Granero Belinchón, RafaelAutoridad Unican
Fecha
2022-09
Derechos
©2022. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00605-021-01623-8
Publicado en
Monatshefte für Mathematik, 2022, 198, 503-516
Editorial
Springer-Verlag
Enlace a la publicación
Resumen/Abstract
In this work we prove that the solution of the Serre-Green-Naghdi equation cannot be globally defined when the interface reaches the impervious bottom tangentially. As a consequence, our result complements the paper Camassa, R., Falqui, G., Ortenzi, G., Pedroni, M., & Thomson, C. Hydrodynamic models and confinement effects by horizontal boundaries. Journal of Nonlinear Science, 29(4), 1445-1498, 2019. Furthermore, we also prove that the solution to the abcd− Boussinesq system can change sign in finite time. Finally, we provide with a proof of a scenario of finite time singularity for the abcd− Boussinesq system. These latter mathematical results are related to the numerics in Bona, and Chen, Singular solutions of a Boussinesq system for water waves. J. Math. Study, 49(3), 205-220, 2016.
Colecciones a las que pertenece