Scholarlink

<p>In this paper, we consider the modified two-component Camassa–Holm system, which is a model to describe the shallow water waves moving over a linear shear flow. By using the Kato’s theory, the local well-posedness of solutions is established for the initial data belonging to the Sobolev space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2573_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="80" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^s\times H^{s-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mi>s</mi> </msup> <mo>×</mo> <msup> <mi>H</mi> <mrow> <mi>s</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2573_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(s&gt;\frac{5}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mo>&gt;</mo> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>. Then, we give a sufficient condition on the initial data to guarantee the occurrence of wave breaking, and obtain the blow-up rate of blow-up solutions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Well-posedness and wave breaking phenomena for the modified two-component Camassa–Holm system

  • 期刊论文

  • 发表日期：

    2025年8月27日

查看全文
  • Xiaowan Li,
  • Shuguan Ji,
  • Yonghui Zhou

摘要

In this paper, we consider the modified two-component Camassa–Holm system, which is a model to describe the shallow water waves moving over a linear shear flow. By using the Kato’s theory, the local well-posedness of solutions is established for the initial data belonging to the Sobolev space \(H^s\times H^{s-1}\) H s × H s - 1 with \(s>\frac{5}{2}\) s > 5 2 . Then, we give a sufficient condition on the initial data to guarantee the occurrence of wave breaking, and obtain the blow-up rate of blow-up solutions.