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<p>This paper is concerned with the derivation of a two-component system modeling shallow-water waves with constant vorticity under the Camassa–Holm scaling from our newly established Green–Naghdi equations with a linear shear. It is worth pointing out that the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2585_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> </InlineEquation> component in this new system is quite different from the previous two-component system due to the effects of both vorticity and larger amplitude. We then establish the local well-posedness of this new system in Besov spaces, and present a blow-up criterion. We finally give a sufficient condition for global strong solutions to the system in some special case.</p>

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Two-component system modeling shallow-water waves with constant vorticity under the Camassa–Holm scaling

  • 期刊论文

  • 发表日期：

    2025年9月13日

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  • Leyi Zhang,
  • Xingxing Liu

摘要

This paper is concerned with the derivation of a two-component system modeling shallow-water waves with constant vorticity under the Camassa–Holm scaling from our newly established Green–Naghdi equations with a linear shear. It is worth pointing out that the \(\rho \) ρ component in this new system is quite different from the previous two-component system due to the effects of both vorticity and larger amplitude. We then establish the local well-posedness of this new system in Besov spaces, and present a blow-up criterion. We finally give a sufficient condition for global strong solutions to the system in some special case.