We study the Cauchy problem with periodic initial data for two dimensional Navier-Stokes equations of compressible fluid flows. We assume that the bulk viscosity coefficient that appears in Navier-Stokes equations depends on the density of the flow. The global existence of solutions with uniform bounds on density is proved when initial data are from the class L infinity ( T2 ) x [W1,2 ( T2 )]2, where Tn=R n/Zn . |