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

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2020-07, Vol.237 (1), p.347-382
Main Authors: Fernández-Dalgo, Pedro Gabriel, Lemarié-Rieusset, Pierre Gilles
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-020-01510-w