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<p>In this paper, we first establish the local existence and uniqueness of strong solutions with initial vacuum to the Cauchy problem of two-dimensional full compressible magnetohydrodynamic system, and then obtain the integrability of velocity and temperature innovatively. Moreover, it is showed that the strong solutions exist globally, provided that the temporal integral of the maximum norm of the divergence of velocity is bounded. The key idea is to utilize some techniques in the theory of singular integrals such as the <i>A</i><sub><i>p</i></sub> weights and the cancellation of singularity.</p>

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Existence and Blowup Criterion of Strong Solutions to Full Compressible Magnetohydrodynamic System with Vacuum in ℝ2

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Bo-qiang Lv,
  • Xue Wang,
  • Peng Zhou

摘要

In this paper, we first establish the local existence and uniqueness of strong solutions with initial vacuum to the Cauchy problem of two-dimensional full compressible magnetohydrodynamic system, and then obtain the integrability of velocity and temperature innovatively. Moreover, it is showed that the strong solutions exist globally, provided that the temporal integral of the maximum norm of the divergence of velocity is bounded. The key idea is to utilize some techniques in the theory of singular integrals such as the Ap weights and the cancellation of singularity.