@article{10902/29575,
year = {2022},
month = {9},
url = {https://hdl.handle.net/10902/29575},
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.},
organization = {H.B. was supported by NRF-2018R1D1A1B07049015. R.G-B was supported by the project ”Mathematical Analysis of Fluids and Applications” with reference PID2019-109348GA-I00/AEI/ 10.13039/501100011033 and acronym “MAFyA” funded by Agencia Estatal de Investigación and the Ministerio de Ciencia, Innovación y Universidades (MICIU). The authors are grateful to Vincent Duchene for fruitful discussions and to David Lannes for useful comments that greatly improved the presentation. Finally, the authors gratefully thank to the Referee for the constructive comments and recommendations which definitely help to improve the readability and quality of the paper.},
publisher = {Springer-Verlag},
publisher = {Monatshefte für Mathematik, 2022, 198, 503-516},
title = {Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems},
author = {Bae, Hantaek and Granero Belinchón, Rafael},
}