A new regularity criterion for weak solutions to the Navier–Stokes equations

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On the regularity of the solutions of the Navier–Stokes equations via one velocity component (2010, background): “The first result in this direction is due to Neustupa et al [10] (see also Zhou’s work [19]), where the authors showed that if u3 ∈ L(0, T ; Ls(R3)), (2)t + (3)s = 1 2 , s ∈ (6, ∞], then the solution is smooth.”
Log Improvement of the Prodi-Serrin Criteria for Navier-Stokes Equations (2007, background): “Let us also cite a condition involving the lower bound of the pressure introduced by Seregin and Sverak in [15], and conditions involving only one of the component of u (see Penel and Pokorny [13], He [5], and Zhou [19]).”