Norm inflation with infinite loss of regularity at general initial data for nonlinear wave equations in Wiener amalgam and Fourier amalgam spaces. (October 2022)

• Record Type: Journal Article
• Authors: Bhimani, Divyang G.; Haque, Saikatul
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: primary 35L05 42B35 -- secondary 35B30; Nonlinear wave equations -- Norm inflation (strong ill-posedness) -- Wiener amalgam spaces -- Fourier amalgam spaces -- Fourier–Lebesgue spaces -- Modulation spaces; 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.2022.113076
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the strong ill-posedness (norm inflation with infinite loss of regularity) for the nonlinear wave equation at every initial data in Wiener amalgam and Fourier amalgam spaces with negative regularity. In particular these spaces contain Fourier–Lebesgue, Sobolev and some modulation spaces. The equations are posed on R d and on torus T d and involve a smooth power nonlinearity. Our results are sharp with respect to well-posedness results of Bényi and Okoudjou (2009) and Cordero and Nicola (2009) in the Wiener amalgam and modulation space cases. In particular, we also complement norm inflation result of Christ, Colliander and Tao (2003) and Forlano and Okamoto (2020) by establishing infinite loss of regularity in the aforesaid spaces.