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

In this paper, it is shown that an analogue in mixed norm spaces of Gagliardo-Nirenberg inequality is valid. 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 corresponding known results.