Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space B¹_∞,1

2023/03/10 by Jinlu Li, Li, Jinlu, Yanghai Yu +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2303.05671

openalex publication_date 2023/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the real-line case, it is shown that both the Camassa--Holm \citeGuo and Novikov equations \citeLi-arx are ill-posed in B_∞,1¹. In this paper, by presenting a new construction of initial data which leads to the norm inflation phenomena, we prove that both the periodic Camassa--Holm and Novikov equations are also ill-posed in B_∞,1¹.

Related

• Ill-posedness of the Novikov equation in the critical Besov space B¹_∞,1(ℝ)
• Ill-posedness for a generalized Camassa-Holm equation with higher-order nonlinearity in the critical Besov space
• Ill-posedness for the Cauchy problem of the modified Camassa-Holm equation in B⁰_∞,1
• Ill-posedness for the Cauchy problem of the Camassa-Holm equation in B¹_∞,1(ℝ)
• Ill-posedness for the Camassa-Holm and related equations in Besov spaces