@Article{JMS-49-205,
author = {Bona , Jerry L. and Chen , Min},
title = {Singular Solutions of a Boussinesq System for Water Waves},
journal = {Journal of Mathematical Study},
year = {2016},
volume = {49},
number = {3},
pages = {205--220},
abstract = {<p style="text-align: justify;">Studied here is the Boussinesq system $$η_t+u_x+(ηu)_x+au_{xxx}-bη_{xxt}=0,$$ $$u_t+η_x+\frac{1}{2}(u²)_x+cη_{xxx}-du_{xxt}=0,$$of partial differential equations. This system has been used in theory and practice as a
model for small-amplitude, long-crested water waves. The issue addressed is whether
or not the initial-value problem for this system of equations is globally well posed.<br/>The investigation proceeds by way of numerical simulations using a computer code
based on a a semi-implicit, pseudo-spectral code. It turns out that larger amplitudes
or velocities do seem to lead to singularity formation in finite time, indicating that the
problem is not globally well posed.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v49n3.16.01},
url = {http://global-sci.org/intro/article_detail/jms/999.html}
}