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<p>In this paper, it is shown that an analogue of the standard Gagliardo–Nirenberg inequality in anisotropic Lebesgue spaces is valid, for which the necessary and sufficient condition is also obtained. As an application, some new criteria for energy conservation of Leray–Hopf weak solutions to the 3D Navier–Stokes equations are established in these spaces, which extend the known corresponding results.</p>

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Gagliardo–Nirenberg inequality in anisotropic Lebesgue spaces and energy equality in the Navier–Stokes equations

  • 期刊论文

  • 发表日期：

    2025年7月13日

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  • Yanqing Wang,
  • Xue Mei,
  • Wei Wei

摘要

In this paper, it is shown that an analogue of the standard Gagliardo–Nirenberg inequality in anisotropic Lebesgue spaces is valid, for which the necessary and sufficient condition is also obtained. As an application, some new criteria for energy conservation of Leray–Hopf weak solutions to the 3D Navier–Stokes equations are established in these spaces, which extend the known corresponding results.