On a regularity criterion for the solutions to the 3D Navier-Stokes equations

By Luigi C. Berselli. Differential and Integral Equations, 2002

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Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor (2010, background): “≤ Cr‖ψ‖ 6−r 2r 2 ‖ψ‖ 3(r−2) 2r H1(Ω) , (10) for every ψ ∈ H(1)(Ω) and every r ∈ [2, 6].”
On the energy equality for the 3D Navier–Stokes equations (2018, background): “then weak solutions are regular, see Beirão da Veiga [3] and also [5] for the problem in a bounded domain.”
Regularity Criteria for the Three-dimensional Navier-Stokes Equations (2008, background): “Most recently, there has been some progress along these lines (see, for example, [2], [3], [15], [18], [19], [21], [41], [42], and references therein) which states, roughly speaking, that a strong solution u exists on the time interval [0, T] for as long as”