Weak solutions for Navier--Stokes equations with initial data in weighted $L^2$ spaces. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2020

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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Dates et versions

hal-02164545 , version 1 (25-06-2019)

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Citer

Pedro Gabriel Fernández-Dalgo, Pierre Gilles Lemarié-Rieusset. Weak solutions for Navier--Stokes equations with initial data in weighted $L^2$ spaces.. Archive for Rational Mechanics and Analysis, 2020, 237 (1), pp.347-382. ⟨10.1007/s00205-020-01510-w⟩. ⟨hal-02164545⟩
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