Calder{ó}n splitting and weak solutions for Navier-Stokes equations with initial data in weighted L p spaces

We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces , using Calder{ó}n splitting L p $Φ$$γ$ $⊂$ L 2 $Φ$ 2 + L r (with some r $∈$ (3, +$∞$)) and energy controls in L 2 $Φ$ 2 .