Citation/Abstract

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 ^∞ ([Special characters omitted.] ) × [ W ^1,2 ([Special characters omitted.] )] ² , where [Special characters omitted.] .