Asymptotic behavior of the energy and pointwise estimates for solutions to the Navier-Stokes equations.
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.
scientific article; zbMATH DE number 2104145
scientific article