On the blow-up criterion of 3D Navier–Stokes equations

In this paper we prove some properties of the maximal solution of Navier–Stokes equations. If the maximum time T ν ∗ is finite, we establish that the growth of ‖ u ( t ) ‖ H ˙ s is at least of the order of ( T ν ∗ − t ) − s / 3 (see Eq. (1.4)), also we give some new blow-up results. Specific properties and standard techniques are used.