Revista Matemática Iberoamericana


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Volume 20, Issue 1, 2004, pp. 223–256
DOI: 10.4171/RMI/387

Published online: 2004-04-30

Asymptotic behavior of the energy and pointwise estimates for solutions to the Navier-Stokes equations

Lorenzo Brandolese[1]

(1) Université Lyon 1, Villeurbanne, France

We study the large time behavior of the energy of a class of Navier-Stokes flows in $\mathbb{R}^n$ $(n\ge2)$ with special symmetries. Inside this class, we construct examples of solutions such that the energy norm decays faster than $t^{-(n+2)/4}$.

Keywords: Navier–Stokes equations, time decay, space decay, symmetric solutions

Brandolese Lorenzo: Asymptotic behavior of the energy and pointwise estimates for solutions to the Navier-Stokes equations. Rev. Mat. Iberoamericana 20 (2004), 223-256. doi: 10.4171/RMI/387