<p>In this paper, we investigate a new regularity criterion for the axisymmetric solution of the 3D inhomogeneous incompressible Navier–Stokes equations. The criterion is slightly supercritical, and its proof relies on a derivative-reduction method and the improved De Giorgi-Nash-Moser iteration for parabolic equations.</p>

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Remarks on regularity criteria for axisymmetric inhomogeneous Navier–Stokes equations

  • Hui Chen,
  • Zijin Li,
  • Ping Zhang

摘要

In this paper, we investigate a new regularity criterion for the axisymmetric solution of the 3D inhomogeneous incompressible Navier–Stokes equations. The criterion is slightly supercritical, and its proof relies on a derivative-reduction method and the improved De Giorgi-Nash-Moser iteration for parabolic equations.