Asymptotic behavior of the energy and pointwise estimates for solutions to the Navier-Stokes equations. (English) Zbl 1057.35026

The aim of the paper is to construct, in any dimension \(n\geq 2\), a class of solutions of the Navier-Stokes equations such that the energy norm decays at infinity larger than \(t^{-(n+2)/4}\). To this end the author studies the large time behaviour of the energy of a class of Navier-Stokes flows with special symmetries in the initial data which are preserved in the solution. In particular, initial data is considered where the components of the initial velocity vector can be obtained one from the other by rotating the space variables.


35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI EuDML


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