Norm inflation for the generalized Boussinesq and Kawahara equations
arXiv:1612.07870 · doi:10.1016/j.na.2017.03.011
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.
19 pages
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