Weak Solutions for Navier–Stokes Equations with Initial Data in Weighted L² Spaces

Abstract:

We show the existence of global weak solutions to the three dimensional Navier–Stokes equations with initial velocity in the weighted spaces Lwγ2, where wγ(x) = (1 + | x|) -γ and 0 < γ≦ 2 , using new energy controls. As an application we give a new proof of the existence of global weak discretely self-similar solutions to the three dimensional Navier–Stokes equations for discretely self-similar initial velocities which are locally square integrable.

Año de publicación:

2020

Keywords:

Fuente:

scopus