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Singularity formation to the 2D Cauchy problem of nonbarotropic magnetohydrodynamic equations without heat conductivity

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  • Xin Zhong

Abstract

The question of whether the two‐dimensional (2D) nonbarotropic compressible magnetohydrodynamic (MHD) equations with zero heat conduction can develop a finite‐time singularity from smooth initial data is a challenging open problem in fluid dynamics and mathematics. Such a problem is interesting in studying global well‐posedness of solutions. In this paper, we proved that, for the initial density allowing vacuum states, the strong solution exists globally if the density and the pressure are bounded from above. Our method relies on weighted energy estimates and a Hardy‐type inequality.

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  • Xin Zhong, 2023. "Singularity formation to the 2D Cauchy problem of nonbarotropic magnetohydrodynamic equations without heat conductivity," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3782-3801, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3782-3801
    DOI: 10.1002/mana.202100292
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