Global weak solutions to the isentropic compressible Navier-Stokes equations with vacuum and unbounded density in a half-plane under Dirichlet boundary conditions

We establish the global existence of a class of weak solutions to the isentropic compressible Navier-Stokes equations in a half-plane with Dirichlet boundary conditions, allowing for vacuum both in the interior and at infinity, under a suitably small initial total energy. The solutions constructed h