On smoothness of L3,∞-solutions to the Navier–Stokes equations up to boundary

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The Navier-Stokes Equations in the Critical Lebesgue Space (2009, background): “That is, roughly speaking, if some scaling invariant quantities are small then the solution is locally regular.”
Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations (2006, background): “Similar regularity criteria have been established near the boundary [36, 12, 28].”
Estimates of suitable weak solutions to the Navier-Stokes equations in critical Morrey spaces (2006, methodology): “ 1 2(R)C 1 3(R)E 1 2(R) i (2.3) for all 0 < R ≤ 1. A kind of a decay estimate for the pressure is the third inequality. There are a several versions of such decay estimate. One of the is proved in [6] and reads D0(r) ≤ c hr 5 2D 0()+ r 2 C() i (2.4) for any 0 < r ≤ ≤ 1. However, in a number”