论文标题
serre-green-naghdi方程的奇异性形成和应用于ABCD-BoussinesQ系统的应用
Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems
论文作者
论文摘要
在这项工作中，我们证明，当界面切向底部到达不透水的底部时，无法在全球定义Serre-Green-Naghdi方程的解。结果，我们的结果补充了论文\ emph {Camassa，R。，Falqui，G。，Ortenzi，G.，Pedroni，M。，\＆Thomson，C。水平边界的水动力模型和限制效应。非线性科学杂志，29（4），1445-1498，2019。}此外，我们还证明，$ abcd- $ boussinesq系统的解决方案可以在有限的时间内更改符号。最后，我们为$ abcd- $ boussinesq系统提供了有限时间奇点的情况。这些后一个数学结果与\ emph {Bona，\＆Chen中的数字有关，这是用于水波的Boussinesq系统的单数解。 J. Math。研究，49（3），205-220，2016}。
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 \emph{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 \emph{Bona, \& Chen, Singular solutions of a Boussinesq system for water waves. J. Math. Study, 49(3), 205-220, 2016}.
