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

Volume 26 / 1999

Takayuki Kobayashi, Wojciech Zajączkowski Applicationes Mathematicae 26 (1999), 159-194 DOI: 10.4064/am-26-2-159-194


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 $H^{2+α,1+α/2}(Ω × ℝ_+)$ and the density belongs to $H^{1+α,1/2+α/2}(Ω× ℝ_+)$, α ∈ (1/2,1).


  • Takayuki Kobayashi
  • Wojciech Zajączkowski

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