Remarks on the global solutions of 3-D Navier-Stokes system with one slow variable
Abstract
By applying Wiegner' method in Wiegner, we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space dimension. As an application of this decay estimate, we give a simplified proof for the global wellposedness result in cg3 for 3-D Navier-Stokes system with one slow variable. Let us also mention that compared with the assumptions for the initial data in cg3, here the assumptions in Theorem slowvarsimplifie are weaker.
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