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<p>This paper establishes a sufficient condition for the finite-time blow-up of smooth solutions to the compressible quantum magnetohydrodynamic (QMHD) system in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^{d}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(d\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. We prove that if the initial density has compact support, then any smooth solution must blow up in finite time.</p>

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Blow-Up of Smooth Solutions to the Compressible Quantum Magnetohydrodynamic System

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Jianwei Yang,
  • Jing Wang

摘要

This paper establishes a sufficient condition for the finite-time blow-up of smooth solutions to the compressible quantum magnetohydrodynamic (QMHD) system in \(\mathbb {R}^{d}\) R d for \(d\ge 3\) d ≥ 3 . We prove that if the initial density has compact support, then any smooth solution must blow up in finite time.