Weak Solutions for Navier–Stokes Equations with Initial Data in Weighted $$L^2$$L2 Spaces

We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces L 2 wγ , where w γ (x) = (1 + |x|) −γ and 0 < γ ≤ 2, using new energy controls. As application we give a new proof of the existence of global weak discretely self-similar solutions of the 3D Navier-Stokes equations for discretely self-similar initial velocities which are locally square inte-grable.