2020/01/31 by Hantaek Bae, Bae, Hantaek, Rafael Granero-Belinchón +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Navier-Stokes equation solutions #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2001.11937
openalex publication_date 2020/01/31 · openalex created_date 2020/02/07 · openalex updated_date 2026/07/28
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.