The second iterate for the Navier–Stokes equation

We consider the iterative resolution scheme for the Navier–Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t . We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch–Tataru solutions; a first step towards weak–strong uniqueness for Koch–Tataru solutions; and finally an instability result in B˙−1 ∞,q, for q >2. © 2008 Elsevier Inc. All rights reserved