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<p>We provide the breakdown mechanism of pressureless gases when the initial vorticity is zero. In other words, the maximum norm of the divergence and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10473_2025_311_Article_IEq1.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Vert u\Vert_{H^{1\over{2}}}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mo fence="false" stretchy="false">∥</mo> <mi>u</mi> <msub> <mo fence="false" stretchy="false">∥</mo> <mrow> <msup> <mi>H</mi> <mrow> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msup> </mrow> </msub> </math></EquationSource> </InlineEquation> control the breakdown of the solution. Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.</p>

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On singularity formation for 3-D zero pressure flow

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Wei Huo

摘要

We provide the breakdown mechanism of pressureless gases when the initial vorticity is zero. In other words, the maximum norm of the divergence and \(\Vert u\Vert_{H^{1\over{2}}}\) ∥ u ∥ H 1 2 control the breakdown of the solution. Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.