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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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/fed7d230b2664312a936e2af85cf76cd |
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| Sumario: | 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. |
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