Continuity properties of the data-to-solution map for the two-component higher order Camassa-Holm system

2018/05/10 by Feng Wang, Wang, Feng, Fengquan Li +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #35B30 #35G25 #35L05 #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.1805.06290

openalex publication_date 2018/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work studies the Cauchy problem of a two-component higher order Camassa-Holm system, which is well-posed in Sobolev spaces H^s(ℝ)× H^s-2(ℝ), s>(7)/(2) and its solution map is continuous. We show that the solution map is Hölder continuous in H^s(ℝ)× H^s-2(ℝ) equipped with the H^r(ℝ)× H^r-2(ℝ)-topology for 1≤ r

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