Non-uniform continuity on initial data for the two-component b-family system in Besov space

2020/12/16 by Desheng Wu, Cui Li, Wu, Xing +3
Mathematics · Physics and Astronomy · #35B30 #35G25 #35Q53 #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.2012.08696

openalex publication_date 2020/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Cauchy problem of a two-component b-family system, which includes the two-component Camassa-Holm system and the two-component Degasperis-Procesi system. It is shown that the solution map of the two-component b-family system is not uniformly continuous on the initial data in Besov spaces B_{p, r}^s-1(ℝ)× B_{p, r}^s(ℝ) with s>max\1+(1)/(p), (3)/(2)\, 1≤ p, r< ∞. Our result covers and extends the previous non-uniform continuity in Sobolev spaces H^s-1(ℝ)× H^s(ℝ) for s>(5)/(2) (Nonlinear Anal., 2014) to Besov spaces.

Related

• Non-uniform continuous dependence on initial data for a two_component Novikov system in Besov space
• A Note on a Generalized Two Component Camassa-Holm System in Sobolev Spaces
• Non-uniform dependence on initial data for the Camassa--Holm equation in Besov spaces: Revisited
• Non-uniform continuity of the generalized Camassa-Holm equation in Besov spaces
• Non-uniform dependence on initial data for the Camassa-Holm equation in the critical Besov space