(untitled) (Journal of Mathematical Study, 2022)
Studied here is the Boussinesq system η_t+u_x+(ηu)_x+au_xxx-bη_xxt=0, u_t+η_x+12(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. 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.