On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations

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Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations (2005, background): “We proved in [43] that the function w(t) satisfies the last estimate for the optimal exponent q = 3 2 .”
On the Regularity Conditions for the Navier-Stokes and Related Equations (2005, methodology): “We note that there are previous papers (see [6, 8, 9, 11, 12]), where the the Triebel-Lizorkin space F s p,q was used for the study of Cauchy problems in the fluid mechanics.”
Strong Solutions To The Incompressible Navier Stokes Equations In The Half Space (2000, methodology): “From these three lemmata, we can deduce the uniqueness result, in the same way as this was done in the whole space [ 3 ].”
Smooth or singular solutions to the Navier-Stokes system ? (2002, background): “This fact is in a perfect agreement with the regularity result for the bilinear term obtained in [ 7 ].”