Estimations a priori et Lipschitz pour le groupe d'évolution des équations de Navier–Stokes

Abstract

Let A be an “admissible” space for the tridimensional Navier–Stokes equations (for example H ̇ 1/2 , L 3, B ̇ −1+3/p p,∞ for p<+∞ or ∇BMO), and let B NS A be the largest ball in A centered at zero such that the elements of H ̇ 1/2∩ B NS A generate global solutions. We prove an a priori estimate for those solutions, as well as a Lipschitz estimate for the mapping from data to such solutions. Those results are based on a general theorem of profile decomposition for solutions of the Navier–Stokes equations associated with bounded sequences of initial data.