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Article Dans Une Revue Journal of Mathematical Fluid Mechanics Année : 2021

Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl

Résumé

We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the existence of regular global solutions when the initial velocity is an axisymmetric vector field without swirl such that both the initial velocity and its vorticity belong to L 2 ((1 + r 2) − γ 2 dx), with r = x 2 1 + x 2 2 and γ ∈ (0, 2).
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Dates et versions

hal-02955438 , version 1 (01-10-2020)
hal-02955438 , version 2 (15-06-2021)

Identifiants

Citer

Pedro Gabriel Fernández-Dalgo, Pierre Gilles Lemarié-Rieusset. Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl. Journal of Mathematical Fluid Mechanics, 2021, 23 (3), pp.76. ⟨10.1007/s00021-021-00603-0⟩. ⟨hal-02955438v2⟩
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