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<p>In this paper, we get a new blowup criterion of the strong solutions to the 3D viscous liquid–gas two-phase flow model with vacuum. More precisely, for the Cauchy problem and Dirichlet problem, we prove that the strong solutions exist globally, provided that the vorticity of velocity satisfies Serrin’s condition and the maximum norm of the divergence of the velocity is bounded. Moreover, for the Navier-slip boundary condition, we show that the maximum norm of the vorticity of velocity or the maximum norm of the divergence of velocity controls the possible breakdown of the strong solutions. The vacuum is allowed to exist here.</p>

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A new blowup criterion for the 3D viscous liquid–gas two-phase flow model with vacuum

  • 期刊论文

  • 发表日期：

    2025年4月2日

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  • Saiguo Xu,
  • Yinghui Zhang

摘要

In this paper, we get a new blowup criterion of the strong solutions to the 3D viscous liquid–gas two-phase flow model with vacuum. More precisely, for the Cauchy problem and Dirichlet problem, we prove that the strong solutions exist globally, provided that the vorticity of velocity satisfies Serrin’s condition and the maximum norm of the divergence of the velocity is bounded. Moreover, for the Navier-slip boundary condition, we show that the maximum norm of the vorticity of velocity or the maximum norm of the divergence of velocity controls the possible breakdown of the strong solutions. The vacuum is allowed to exist here.