Norm inflation for nonlinear wave equations with infinite loss of regularity in Wiener amalgam spaces

Divyang G. Bhimani, Saikatul Haque

Published 2021-06-25Version 1

We study the strong ill-posedness (norm inflation with infinite loss of regularity) for the nonlinear wave equation in Wiener amalgam, modulation and Fourier-Lebesgue spaces with negative regularity. Our results are sharp and complement well-posedness results of B\'enyi and Okoudjou (2009) and Cordero and Nicola (2009) in these spaces. 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.