Quantitative robustness of regularity for 3D Navier-Stokes system in ${\dot{H}}^{\alpha }$-spaces

We present stability and regularity results for the $3$D incompressible Navier-Stokes system in a periodic box, in ${\dot{H}}^{\alpha }$ spaces, with $\alpha \in [1\mathrm{/}2,1]$. A special attention is paid to obtaining quantitative results, i.e. ones with explicit or at least computable constants, and to scaling.