Quantitative robustness of regularity for 3D Navier-Stokes system in dot H^α-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 $\alpha\in\big[{1/2},1\big]$. A special attention is paid to obtaining quantitative results, i.e. ones with explicit or at least computable constants, and to scaling.