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For periodic initial data with initial density, we establish the globalexistence and uniqueness of strong and classical solutions for thetwo-dimensional compressible Navier-Stokes equations with no restrictions onthe size of initial data provided the shear viscosity is a positive constantand the bulk one is $\lam=\rho^{\b}$ with $\b>1.$

Global classical solution to the Cauchy problem of 2D baratropic compressible Navier-Stokes system with large initial data