Advanced Search

Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ ${ℝ}^3$ 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 $L_2$-approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to $H^{2+\alpha ,1+\alpha /2}\left(\Omega \times {ℝ}_{+}\right)$ and the density belongs to $H^{1+\alpha ,1/2+\alpha /2}\left(\Omega \times {ℝ}_{+}\right)$, α ∈ (1/2,1).