Existence of discretely self-similar solutions to the Navier-Stokes equations for initial value in $L_{loc}^2({\mathbb{R}}^3)$

Abstract

We prove the existence of a forward discretely self-similar solutions to the Navier-Stokes equations in ${\mathbb{R}}^3\times (0,+\infty )$ for a discretely self-similar initial velocity belonging to $L_{loc}^2({\mathbb{R}}^3)$.

25 pages