Norm inflation for BBM equation in Fourier amalgam and Wiener amalgam spaces with negative regularity

2021/10/04 by Divyang G. Bhimani, Bhimani, Divyang G., Saikatul Haque +1
Mathematics · Physics and Astronomy · #35Q55 #35R25 (primary) #42B35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2110.01553

openalex publication_date 2021/10/04 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

We consider Benjamin-Bona-Mahony (BBM) equation of the form u_t+u_x+uu_x-u_xxt=0, (x, t)∈ M× \mathbb R where M= \mathbb T or \mathbb R. We establish norm inflation (NI) with infinite loss of regularity at general initial data in Fourier amalgam and Wiener amalgam spaces with negative regularity. This strengthen several known NI results at zero initial data in H^s(\mathbb T) established by Bona-Dai (2017) and ill-posedness result established by Bona-Tzvetkov (2008) and Panthee (2011) in H^s(\mathbb R). Our result is sharp with respect to local well-posedness result of Banquet-Villamizar-Roa (2021) in modulation spaces M^2,1_s(\mathbb R) for s≥ 0.

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