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Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ R with the boundary slip condition is proved. The solution is close to an equilibrium solution. The proof is based on the energy method. Moreover, in the L2-approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to H(Ω ×R+) and the density belongs to H(Ω × R+), α ∈ (1/2, 1).

On global motion of a compressible barotropic viscous fluid with boundary slip condition