A note on a regularity criterion for the Navier–Stokes equations

Zdeněk Skalák Annales Polonici Mathematici MSC: Primary 35Q30; Secondary 76D05. DOI: 10.4064/ap180826-22-11 Published online: 23 April 2019


We show that if $u$ is a solution of the Navier–Stokes equations in the whole three-dimensional space and $\partial _3 u \in L^p(0,T;L^q(\mathbb {R}^3))$, $T \gt 0$, where $2/p+3/q=1+3/q$ and $q \in (3,10/3]$, then $u$ is regular on $(0,T]$.


  • Zdeněk SkalákInstitute of Hydrodynamics
    Czech Academy of Sciences
    16612 Praha, Czech Republic

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