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

2021/06/25 by Divyang G. Bhimani, Bhimani, Divyang G., Saikatul Haque +1
Mathematics · #35B30 (secondary) #35L05 #42B35 (primary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2106.13635

openalex publication_date 2021/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbb R^d and on torus \mathbb 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.

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