Scholarlink

<p>This paper investigates the isentropic compressible Euler–Korteweg system with a density-dependent capillary coefficient. Assuming the initial density is compactly supported and the radius of its support grows at most polynomially in time (i.e., <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>R</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>≤</mo> <msub> <mi>C</mi> <mn>1</mn> </msub> <msup> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>α</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">$R(t) \leq C_{1}(1+t)^{\alpha}$</EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>α</mi> <mo>&lt;</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\alpha &lt; 1$</EquationSource> </InlineEquation>), we prove that smooth solutions must blow up in finite time and establish an explicit upper bound for the blow-up time.</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

Finite-time blow-up for the compressible Euler–Korteweg system with density-dependent capillarity

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年11月21日

查看全文
  • Xiaoxia Yang,
  • Jianwei Yang

摘要

This paper investigates the isentropic compressible Euler–Korteweg system with a density-dependent capillary coefficient. Assuming the initial density is compactly supported and the radius of its support grows at most polynomially in time (i.e., R ( t ) ≤ C 1 ( 1 + t ) α $R(t) \leq C_{1}(1+t)^{\alpha}$ with α < 1 $\alpha < 1$ ), we prove that smooth solutions must blow up in finite time and establish an explicit upper bound for the blow-up time.