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Pré-Publication, Document De Travail Année : 2004

On Periodic 3D Navier-Stokes Equations when the initial velocity is in L2 and the initial vorticity is in L1.

Résumé

This paper is devoted to the 3D Navier-Stokes equations in a periodic case. Assuming that the initial data u0 is in L2x while the initial vorticity ω0=×u0 is in L1x, we prove the existence of a distributional solution (u,p) to the Navier-Stokes equations such that uL2t(H1x)Lt(L2x)Lpt(W2,px)p<5/4, and ω=×uLt(L1x)Lpt(W1,px)p<5/4,pL5/4t(W1,5/4x). The main remark of the paper is that the equation for the vorticity can be considered as a parabolic equation with a right hand side in L1t,x. Thus one can use tools of the renormalization theory. Studying approximations deduced from a Large Eddy Simulations model, we focus our attention in passing to the limit in the equation for the vorticity. Finally, we look for sufficient conditions yielding uniqueness of the limit.
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Dates et versions

hal-00001339 , version 1 (23-03-2004)

Identifiants

  • HAL Id : hal-00001339 , version 1

Citer

Roger Lewandowski. On Periodic 3D Navier-Stokes Equations when the initial velocity is in L2 and the initial vorticity is in L1.. 2004. ⟨hal-00001339⟩
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