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

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, & Chen, Singular solutions of a Boussinesq system for water waves. J. Math. Study, 49(3), 205-220, 2016.

 Fuente: Monatshefte für Mathematik, 2022, 198, 503-516

 Editorial: Springer-Verlag

 Fecha de publicación: 01/09/2022

 Nº de páginas: 12

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00605-021-01623-8

 ISSN: 0026-9255,1436-5081

 Proyecto español: PID2019-109348GA-I00

 Url de la publicación: https://doi.org/10.1007/s00605-021-01623-8

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