Scholarlink

<p>We consider the inhomogeneous (or density dependent) incompressible Euler equations in a three-dimensional periodic domain. We construct density <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varrho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϱ</mi> </math></EquationSource> </InlineEquation> and velocity <i>u</i> such that, for any <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha &lt;1/7\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>&lt;</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>7</mn> </mrow> </math></EquationSource> </InlineEquation>, both of them are <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-Hölder continuous and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((\varrho , u)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>ϱ</mi> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is a weak solution to the underlying equations. The proof is based on typical convex integration techniques using Mikado flows as building blocks. As a main novelty with respect to the related literature, our result produces a Hölder continuous density.</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

Non-uniqueness of Hölder continuous solutions for inhomogeneous incompressible Euler flows

  • 期刊论文

  • 发表日期：

    2026年3月7日

查看全文
  • Vikram Giri,
  • Ujjwal Koley

摘要

We consider the inhomogeneous (or density dependent) incompressible Euler equations in a three-dimensional periodic domain. We construct density \(\varrho \) ϱ and velocity u such that, for any \(\alpha <1/7\) α < 1 / 7 , both of them are \(\alpha \) α -Hölder continuous and \((\varrho , u)\) ( ϱ , u ) is a weak solution to the underlying equations. The proof is based on typical convex integration techniques using Mikado flows as building blocks. As a main novelty with respect to the related literature, our result produces a Hölder continuous density.