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<p>In (Moffatt J Fluid Mech 38:117–129, 1969), Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solutions to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in Onsager-type spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="28_2024_1052_Article_IEq1.gif" Format="GIF" Height="29" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\({B}^{1/3}_{p,c(\mathbb {N})}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mi>B</mi> </mrow> <mrow> <mi>p</mi> <mo>,</mo> <mi>c</mi> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">N</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </msubsup> </math></EquationSource> </InlineEquation> guarantee the conservation of helicity. To the best knowledge of authors, this is the first result concerning the helicity conservation of weak solutions to the compressible Euler equations. Moreover, the parallel results of homogeneous incompressible Euler equations are also obtained, which generalized the previous known results.</p>

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Analytical validation of the helicity conservation for the compressible Euler equations

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Yulin Ye,
  • Wei Wei,
  • Yanqing Wang

摘要

In (Moffatt J Fluid Mech 38:117–129, 1969), Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solutions to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in Onsager-type spaces \({B}^{1/3}_{p,c(\mathbb {N})}\) B p , c ( N ) 1 / 3 guarantee the conservation of helicity. To the best knowledge of authors, this is the first result concerning the helicity conservation of weak solutions to the compressible Euler equations. Moreover, the parallel results of homogeneous incompressible Euler equations are also obtained, which generalized the previous known results.