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

Abstract

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