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

2022/04/15 by Wang, Yanqing, Mei, Xue, Wei, Wei
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2204.07479

Abstract

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.

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