On the stability of global solutions to Navier–Stokes equations in the space

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Wellposedness and stability results for the Navier-Stokes equations in ${\mathbf R}^{3}$ (2006, background): “bal solutions. It is known since [11] that any initial data in B˙ −1+3 p p,∞ giving rise to a unique global solution is stable: a small perturbation of that data also generates a global solution (see [1] for the case of BMO−1). Here we present a stability result where the perturbation is as large as”
Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations (2005, background): “See also [2,95,96,145] for related results in this direction.”
Multipliers, paramultipliers, and weak-strong uniqueness for the Navier-Stokes equations (2006, background): “Then (v ·∇u) can be written as a (finite) sum of functions which belong to one of the spaces L 2 2−α Ḣ−α, for some α ∈ [0, 1].”