Norm inflation for the generalized Boussinesq and Kawahara equations

TL;DR

This paper demonstrates norm inflation, indicating ill-posedness, for the generalized Boussinesq and Kawahara equations, extending previous results by establishing more general initial data conditions.

Contribution

It improves existing ill-posedness results by proving norm inflation for broader classes of initial data in these equations.

Findings

Norm inflation occurs for the generalized Boussinesq equations.

Norm inflation occurs for the Kawahara equation.

The results extend previous ill-posedness findings.

Abstract

We consider ill-posedness of the Cauchy problem for the generalized Boussinesq and Kawahara equations. We prove norm inflation with general initial data, an improvement over the ill-posedness results by Geba et al., Nonlinear Anal. 95 (2014), 404-413 for the generalized Boussinesq equations and by Kato, Adv. Differential Equations 16 (2011), no. 3-4, 257-287 for the Kawahara equation.