Norm inflation for the generalized Boussinesq and Kawahara equations. (English) Zbl 1368.35250
Summary: 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 D.-A. Geba et al. [ibid. 95, 404–413 (2014; Zbl 1286.35228)] for the generalized Boussinesq equations and by T. Kato [Adv. Differ. Equ. 16, No. 3–4, 257–287 (2011; Zbl 1298.35176)] for the Kawahara equation.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35R25 | Ill-posed problems for PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
Boussinesq equation; Kawahara equation; ill-posedness; norm inflation; general initial dataReferences:
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