On The Role Of Anisotropy In The Weak Stability Of The Navier-Stokes System
Résumé
In this article, we investigate the weak stability for the three dimensional incompressible Navier-Stokes system. Because of the invariances of this system, a positive answer in general to this question would imply global regularity for any data. Thus some restrictions have to be imposed to hope to prove such a weak openness result. The result we prove in this paper solves this issue under anisotropy assumption. To achieve our goal, we write a new kind of profile decomposition and establish global existence results for the Navier-Stokes system associated with new classes of arbitrarily large initial data generalizing the examples dealt with in [14, 15, 16].
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