2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163789We 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 $B^{-1}_{\infty,q}$, for q>2.13 pagesAnalysis of PDEs35Q30 ; 42B25 ; 42B99text