Norm inflation for the generalized Boussinesq and Kawahara equations. (July 2017)

• Record Type: Journal Article
• Authors: Okamoto, Mamoru
• Is Part Of: Nonlinear analysis. Volume 157(2017)
• Page Start: 44
• Page End: 61
• Publication Date: 2017-07
• Subjects: 35Q55 -- 35B30; Boussinesq equation -- Kawahara equation -- Ill-posedness -- Norm inflation -- General initial data; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.03.011
• Languages: English
• ISSNs: 0362-546X

Abstract

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. (2014) for the generalized Boussinesq equations and by Kato (2011) for the Kawahara equation.