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<p>This paper investigates the integrable two-component Camassa–Holm system, which features cubic nonlinearity. Employing both the system’s intrinsic structure and its two conserved quantities, we derive two distinct nonlinear estimates for the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation>-norm of the solution during its existence. Then, based on these estimates, we establish two new blow-up results. Finally, using moderate weight functions, we analyze the asymptotic behaviors of strong solutions.</p>

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Blow-up and asymptotics for an integrable cubic two-component Camassa–Holm system

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Xuanxuan Han,
  • JinRong Wang

摘要

This paper investigates the integrable two-component Camassa–Holm system, which features cubic nonlinearity. Employing both the system’s intrinsic structure and its two conserved quantities, we derive two distinct nonlinear estimates for the \(L^\infty \) L ∞ -norm of the solution during its existence. Then, based on these estimates, we establish two new blow-up results. Finally, using moderate weight functions, we analyze the asymptotic behaviors of strong solutions.