Weak solutions for Navier--Stokes equations with initial data in weighted $L^2$ spaces.
Résumé
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.
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