Blowing-Up Solutions of the Shallow Water Equations

Abstract

In the paper, we study the question about global unsolvability of the Kawahara and Kaup-Kupershmidt shallow water equations in a bounded domain. For certain initial-boundary-value problems of the shallow-water equations, we establish the necessary conditions for the existence of global solutions. The proof of the results is based on the nonlinear capacity method. In closing, we provide some examples.