Breakdown of a shallow water equation.

*(English)*Zbl 0959.35140The author discusses the following two questions respecting the shallow water equations:

1. When does the shallow water flow breakdown? 2. How does the shallow water equation breakdown? To answer these questions he studies the 1D equation $\partial v/\partial t+v(\partial v/\partial x)+\partial p/\partial x=0$ with “pressure” $p\left(x\right)=(1/2){\int}_{-\infty}^{\infty}{e}^{-|x-y|}({v}^{2}+{v}^{\text{'}}{}^{2}/2)dy$.

The introductory part of the paper is very useful for the interested reader, where he can find a historical sketch of the problem, the obtained results, and relations to other fields of mathematics.

Reviewer: Vasile Ionescu (Bucureşti)