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

Takayuki Kobayashi; Wojciech Zajączkowski

Applicationes Mathematicae (1999)

- Volume: 26, Issue: 2, page 159-194
- ISSN: 1233-7234

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topKobayashi, Takayuki, and Zajączkowski, Wojciech. "On global motion of a compressible barotropic viscous fluid with boundary slip condition." Applicationes Mathematicae 26.2 (1999): 159-194. <http://eudml.org/doc/219232>.

@article{Kobayashi1999,

abstract = {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).},

author = {Kobayashi, Takayuki, Zajączkowski, Wojciech},

journal = {Applicationes Mathematicae},

keywords = {Hilbert-Besov spaces; compressible barotropic viscous fluid; boundary slip condition; global existence; global-in-time existence of solutions; viscous compressible barotropic fluid; slip boundary condition; energy method},

language = {eng},

number = {2},

pages = {159-194},

title = {On global motion of a compressible barotropic viscous fluid with boundary slip condition},

url = {http://eudml.org/doc/219232},

volume = {26},

year = {1999},

}

TY - JOUR

AU - Kobayashi, Takayuki

AU - Zajączkowski, Wojciech

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

JO - Applicationes Mathematicae

PY - 1999

VL - 26

IS - 2

SP - 159

EP - 194

AB - 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).

LA - eng

KW - Hilbert-Besov spaces; compressible barotropic viscous fluid; boundary slip condition; global existence; global-in-time existence of solutions; viscous compressible barotropic fluid; slip boundary condition; energy method

UR - http://eudml.org/doc/219232

ER -

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