Mathematica Slovaca ( IF 0.654 ) Pub Date : 2020-07-24 , DOI: 10.1515/ms-2017-0400
Jamel Benameur; Lotfi Jlali

In this paper, we prove a global well-posedness of the three-dimensional incompressible Navier-Stokes equation under initial data, which belongs to the Lei-Lin-Gevrey space $Za,σ−1$(ℝ3) and if the norm of the initial data in the Lei-Lin space 𝓧−1 is controlled by the viscosity. Moreover, we will show that the norm of this global solution in the Lei-Lin-Gevrey space decays to zero as time approaches to infinity.

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