In this paper, we study the global regularity of large solutions with vacuum to the two-dimensional compressible Navier-Stokes equations on \({{\mathbb T}^2} = {{\mathbb R}^2}/{{\mathbb Z}^2}\) , when the volume (bulk) viscosity coefficient ν is sufficiently large. It first fixes a flaw in Danchin and Mucha (2023), which concerns the ν-independent global t-weighted estimates of the solutions. Amending the proof requires nontrivial mathematical analysis. As a by-product, the incompressible limit with an explicit rate of convergence is shown, when the volume viscosity tends to infinity. In contrast to the studies due to Danchin and Mucha (2017, 2019), where vacuum was excluded, the convergence rate of the incompressible limit is obtained for the global solutions with vacuum, based on some t-growth and singular t-weighted estimates.
