Calder{\'o}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{\'o}n splitting L p $\Phi$$\gamma$ $\subset$ L 2 $\Phi$ 2 + L r (with some r $\in$ (3, +$\infty$)) and energy controls in L 2 $\Phi$ 2 .