Global weak solutions and incompressible limit to the isentropic compressible Navier-Stokes equations in 2D bounded domains with ripped density and large initial data

This paper is a continuation of our previous work (arXiv:2507.03505), where the global existence and incompressible limit of weak solutions to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and large initial data were established. We extend such results to the case of two-dimensional bounded convex domains under a Navier-slip boundary condition. To overcome difficulties in the presence of a curved boundary, some new estimates based on the effective viscous flux and a Desjardins-type logarithmic interpolation inequality play decisive roles.