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<p>This paper investigates the barotropic compressible magnetohydrodynamic equations within a three-dimensional bounded domain encompassing vacuum states, subject to slip boundary conditions. When the fluid is nearly isothermal (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma &gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> sufficiently close to 1), we show global existence of classical solutions for initial data with arbitrarily large energy and possible vacuum. Moreover, we prove that these solutions demonstrate exponential energy decay at rates inversely proportional to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. Finally, we show that when the initial state contains a vacuum, the oscillations of the density will grow without bound at an exponential rate.</p>

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Nishida-Smoller Type Large Solutions for the Compressible Magnetohydrodynamic Equations in 3D Bounded Domain

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Jinxia Liu,
  • Yinghui Zhang

摘要

This paper investigates the barotropic compressible magnetohydrodynamic equations within a three-dimensional bounded domain encompassing vacuum states, subject to slip boundary conditions. When the fluid is nearly isothermal ( \(\gamma >1\) γ > 1 sufficiently close to 1), we show global existence of classical solutions for initial data with arbitrarily large energy and possible vacuum. Moreover, we prove that these solutions demonstrate exponential energy decay at rates inversely proportional to \(\gamma \) γ . Finally, we show that when the initial state contains a vacuum, the oscillations of the density will grow without bound at an exponential rate.