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<p>Due to the singular nonlinear Hall term, the non-resistive electron magnetohydrodynamics (MHD) is not known to be locally well-posed in general. In this paper we consider the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\frac{1}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>D electron MHD with either horizontal or vertical resistivity and show local well-posedness in Sobolev spaces.</p>

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Well-Posedness of the Electron MHD with Partial Resistivity

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  • 发表日期：

    2026年7月16日

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  • Hassan Babaei,
  • Mimi Dai

摘要

Due to the singular nonlinear Hall term, the non-resistive electron magnetohydrodynamics (MHD) is not known to be locally well-posed in general. In this paper we consider the \(2\frac{1}{2}\) 2 1 2 D electron MHD with either horizontal or vertical resistivity and show local well-posedness in Sobolev spaces.