Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations

Abstract

We prove that there exist infinitely many distributional solutions with infinite kinetic energy to the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $. We prove as well the existence of infinitely many distributional solutions for Burgers equation in $ \mathbb{R} $.