Electron. J. Diff. Equ., Vol. 2016 (2016), No. 104, pp. 1-13.

Long time decay for 3D Navier-Stokes equations in Sobolev-Gevrey spaces

Jamel Benameur, Lotfi Jlali

Abstract:
In this article, we study the long time decay of global solution to 3D incompressible Navier-Stokes equations. We prove that if is a global solution, where $H^1_{a,\sigma}(\mathbb{R}^3)$ is the Sobolev-Gevrey spaces with parameters a>0 and $\sigma>1$, then $\|u(t)\|_{H^1_{a,\sigma}(\mathbb{R}^3)}$ decays to zero as time approaches infinity. Our technique is based on Fourier analysis.

Submitted February 2, 2016. Published April 21, 2016.
Math Subject Classifications: 35Q30, 35D35.
Key Words: Navier-Stokes Equation; critical spaces; long time decay.

Show me the PDF file (234 KB), TEX file for this article.

Jamel Benameur
Institut Supérieur des Sciences Appliquées
et de Technologie de Gabès
Université de Gabès, Tunisia
email: jamelbenameur@gmail.com
Lotfi Jlali
Faculté de Sciences Mathématiques,
Physiques et Naturelles de Tunis
Université de Tunis
El Manar, Tunisia
email: lotfihocin@gmail.com

Return to the EJDE web page