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

Brandolese, Lorenzo

Rev. Mat. Iberoam. 20, No. 1, 223-256 (2004).

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.

Reviewer: Uwe Kähler (Aveiro)

MSC:

35Q30	Navier-Stokes equations
35B40	Asymptotic behavior of solutions to PDEs
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

Navier-Stokes equations; energy estimates; symmetric weak solutions; large time behaviour

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