Small ${\dot{B}}_{\mathrm{\infty },\mathrm{\infty }}^{-1}$ implies regularity

We show that smallness of ${\dot{B}}_{\mathrm{\infty },\mathrm{\infty }}^{-1}$ norm of solution to $d$-dimensional ($d\ge 3$) incompressible Navier-Stokes prevents blowups.