Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces

In this paper, we study the long time decay of global solution to the 3D incompressible Navier-Stokes equations. We prove that if u∈C(R+,X−1,σ(R3))u\in {\mathcal{C}}\left({{\mathbb{R}}}^{+},{{\mathcal{X}}}^{-1,\sigma }\left({{\mathbb{R}}}^{3})) is a global solution to the considered equation, where...

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Autor principal:	Jlali Lotfi
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	navier-stokes equations critical spaces long time decay 35q30 35d35 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/fed7d230b2664312a936e2af85cf76cd
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id	oai:doaj.org-article:fed7d230b2664312a936e2af85cf76cd
record_format	dspace
spelling	oai:doaj.org-article:fed7d230b2664312a936e2af85cf76cd2021-12-05T14:10:53ZLong time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces2391-545510.1515/math-2021-0060https://doaj.org/article/fed7d230b2664312a936e2af85cf76cd2021-08-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0060https://doaj.org/toc/2391-5455In this paper, we study the long time decay of global solution to the 3D incompressible Navier-Stokes equations. We prove that if u∈C(R+,X−1,σ(R3))u\in {\mathcal{C}}\left({{\mathbb{R}}}^{+},{{\mathcal{X}}}^{-1,\sigma }\left({{\mathbb{R}}}^{3})) is a global solution to the considered equation, where Xi,σ(R3){{\mathcal{X}}}^{i,\sigma }\left({{\mathbb{R}}}^{3}) is the Fourier-Lei-Lin space with parameters i=−1i=-1 and σ≥−1\sigma \ge -1, then ‖u(t)‖X−1,σ\Vert u\left(t){\Vert }_{{{\mathcal{X}}}^{-1,\sigma }} decays to zero as time goes to infinity. The used techniques are based on Fourier analysis.Jlali LotfiDe Gruyterarticlenavier-stokes equationscritical spaceslong time decay35q3035d35MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 898-908 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	navier-stokes equations critical spaces long time decay 35q30 35d35 Mathematics QA1-939
spellingShingle	navier-stokes equations critical spaces long time decay 35q30 35d35 Mathematics QA1-939 Jlali Lotfi Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces
description	In this paper, we study the long time decay of global solution to the 3D incompressible Navier-Stokes equations. We prove that if u∈C(R+,X−1,σ(R3))u\in {\mathcal{C}}\left({{\mathbb{R}}}^{+},{{\mathcal{X}}}^{-1,\sigma }\left({{\mathbb{R}}}^{3})) is a global solution to the considered equation, where Xi,σ(R3){{\mathcal{X}}}^{i,\sigma }\left({{\mathbb{R}}}^{3}) is the Fourier-Lei-Lin space with parameters i=−1i=-1 and σ≥−1\sigma \ge -1, then ‖u(t)‖X−1,σ\Vert u\left(t){\Vert }_{{{\mathcal{X}}}^{-1,\sigma }} decays to zero as time goes to infinity. The used techniques are based on Fourier analysis.
format	article
author	Jlali Lotfi
author_facet	Jlali Lotfi
author_sort	Jlali Lotfi
title	Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces
title_short	Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces
title_full	Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces
title_fullStr	Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces
title_full_unstemmed	Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces
title_sort	long time decay for 3d navier-stokes equations in fourier-lei-lin spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/fed7d230b2664312a936e2af85cf76cd
work_keys_str_mv	AT jlalilotfi longtimedecayfor3dnavierstokesequationsinfourierleilinspaces
_version_	1718371639826055168

Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces

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