Global weak solutions with higher regularity to the compressible isentropic Navier-Stokes equations in the half-plane under a slip boundary condition

We prove the global existence of weak solutions to the compressible isentropic Navier-Stokes equations with vacuum in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large. In particular, the initial data can be arbitrarily large and the regularity of solutions is stronger than Lions-Feireisl's weak solutions with general finite-energy initial data. Our method relies on a Desjardins-type logarithmic interpolation inequality and some new techniques based on the effective viscous flux.