Global existence of weak solutions to 3D Navier-Stokes IBVP with non-decaying initial data in exterior domains

We consider the Navier-Stokes initial boundary value problem in 3D-exterior domains with non-decaying initial data. We investigate the existence of weak solutions defined for all t > 0 for large non-decaying initial data. To achieve the result, we extend the half-space technique developed by Maremonti and Shimizu (2018) [26] to the case of an exterior domain