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A Blow-Up Criterion for the Density-Dependent Incompressible Magnetohydrodynamic System with Zero Viscosity

Author

Listed:
  • Kunlong Shi

    (College of Sciences, Nanjing Forestry University, Nanjing 210037, China)

  • Jishan Fan

    (Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China)

  • Gen Nakamura

    (Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan)

Abstract

In this paper, we provide a blow-up criterion for the density-dependent incompressible magnetohydrodynamic system with zero viscosity. The proof uses the L p -method and the Kato–Ponce inequalities in the harmonic analysis. The novelty of our work lies in the fact that we deal with the case in which the resistivity η is positive.

Suggested Citation

  • Kunlong Shi & Jishan Fan & Gen Nakamura, 2024. "A Blow-Up Criterion for the Density-Dependent Incompressible Magnetohydrodynamic System with Zero Viscosity," Mathematics, MDPI, vol. 12(10), pages 1-8, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1510-:d:1393182
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