Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain

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A new regularity criterion for weak solutions to the Navier–Stokes equations (2005, background): “For the regularity criteria in terms of the gradient of velocity or the pressure, we refer to [1, 2, 4, 6, 7, 26, 27, 28].”
On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space (2010, background): “Later, Zhou extended the criteria in terms of the pressure and its gradient to a general domain [33], and Zhou [34, 35] and Struwe [27] obtained regularity criteria for weak solutions in terms of the gradient of pressure.”
Two regularity criteria for the 3D MHD equations (2009, unknown): “, [3],[4],[5],[6],[8],[9],[10],[12], [14],[15],[20],[21],[25],[29],[30], [31],[32],[37],[41],[42],[44],[46],[53],[54]).”
On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure (2007, background): “However, similar to Berselli–Galdi [5], Zhou [26], [28] our proof of Theorem 1.3 requires the estimates ||p||Lq ≤ C||u|| 2 L2q , 1 q ∞, (6) and ||∇p||Lq ≤ C|||∇u||u|||Lq , 1 q ∞, (7) which only seem to be available when either Ω = Rn or in the periodic setting.”
Remark on a regularity criterion in terms of pressure for the Navier-Stokes equations (2011, result): “Regularity results including assumptions on the pressure have been given by Kaniel [8], and more recently a final result has been obtained by Berselli and Galdi [3] (a much simpler proof was given by Zhou [21], very recently).”