Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces

  • 1 Faculté des Sciences de Gabès, Université de Gabès, Gabès, Tunisia
  • 2 Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis, Université de Tunis El Manar, Tunis, Tunisia
Jamel Benameur and Lotfi Jlali
  • Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis, Université de Tunis El Manar, Tunis, Tunisia
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Abstract

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,σ1(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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Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process.

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