WELL-POSEDNESS AND ANALYTICITY FOR AN INTEGRABLE TWO-COMPONENT SYSTEM WITH CUBIC NONLINEARITY

2013/12/01 by YONGSHENG MI, Yongsheng Mi, Chunlai Mu +1 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Applied mathematics #Besov space #Cauchy distribution #Component (thermodynamics) #Computer science #Initial value problem #Integrable system #Interpolation space #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #Range (aeronautics) #Space (punctuation)

paper · doi:10.1142/s0219891613500252

published in Journal of Hyperbolic Differential Equations 10(04), 703-723 (World Scientific)

crossref issued 2013/12/01 · crossref published 2013/12/01 · crossref published-print 2013/12/01 · openalex publication_date 2013/12/01 · crossref published-online 2014/01/22 · crossref created 2014/01/23 · crossref deposited 2020/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05 · crossref indexed 2026/08/05

Abstract

We study the Cauchy problem associated with a new integrable two-component system with cubic nonlinearity, which was recently proposed by Song, Qu and Qiao. We establish the local well-posedness in a range of the Besov spaces. Moreover, for analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time, which extend a result by Danchin, and Himonas et al. to more complex equations.

Citations

• Global Conservative Solutions of the Camassa–Holm Equation
• Singular solutions of a modified two-component Camassa-Holm equation
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• Two-component CH system: Inverse Scattering, Peakons and Geometry
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Wave breaking for nonlinear nonlocal shallow water equations