Scholarlink

<p>In this paper we investigate the two-component nonlinear dispersive wave equation on the real line. We establish a blow-up criterion for the system of coupled equations under certain natural initial profiles. The obtained criterion is only involved in the initial values <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(u_{0}\left( x_{0}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>u</mi> <mn>0</mn> </msub> <mfenced close=")" open="("> <msub> <mi>x</mi> <mn>0</mn> </msub> </mfenced> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(u_{0}^{\prime }\left( x_{0}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>u</mi> <mrow> <mn>0</mn> </mrow> <mo>′</mo> </msubsup> <mfenced close=")" open="("> <msub> <mi>x</mi> <mn>0</mn> </msub> </mfenced> </mrow> </math></EquationSource> </InlineEquation> at a single point <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(x_{0}\in \mathbb {R}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>∈</mo> <mi mathvariant="double-struck">R</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></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

Blow-up criteria for some two-component shallow water wave system

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月24日

查看全文
  • Pelin Ayşe Gökgöz,
  • Emil Novruzov

摘要

In this paper we investigate the two-component nonlinear dispersive wave equation on the real line. We establish a blow-up criterion for the system of coupled equations under certain natural initial profiles. The obtained criterion is only involved in the initial values \(u_{0}\left( x_{0}\right) \) u 0 x 0 and \(u_{0}^{\prime }\left( x_{0}\right) \) u 0 ′ x 0 at a single point \(x_{0}\in \mathbb {R}.\) x 0 ∈ R .