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<p>We investigate the Cauchy problem of incompressible inhomogeneous heat-conducting magnetohydrodynamic equations with temperature-dependent viscosity and resistivity coefficients over the whole space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>. By obtaining some key <i>a priori</i> algebraic decay-in-time rates of the solution, we establish the existence of a unique global strong solution under some smallness condition. In particular, there is no need to require any smallness restriction on the initial density which contains vacuum states and even has compact support.</p>

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Global well-posedness to the 3D Cauchy problem of inhomogeneous heat-conducting magnetohydrodynamic equations with temperature-dependent viscosity and resistivity coefficients

  • 期刊论文

  • 发表日期：

    2026年1月30日

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  • Zihe Wen,
  • Xin Zhong

摘要

We investigate the Cauchy problem of incompressible inhomogeneous heat-conducting magnetohydrodynamic equations with temperature-dependent viscosity and resistivity coefficients over the whole space \(\mathbb {R}^3\) R 3 . By obtaining some key a priori algebraic decay-in-time rates of the solution, we establish the existence of a unique global strong solution under some smallness condition. In particular, there is no need to require any smallness restriction on the initial density which contains vacuum states and even has compact support.