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 $\mathrm{\Phi }$$\gamma$ $\subset$ L 2 $\mathrm{\Phi }$ 2 + L r (with some r $\in$ (3, +$\mathrm{\infty }$)) and energy controls in L 2 $\mathrm{\Phi }$ 2 .