Displaying similar documents to “Diffusion on viscous fluids. Existence and asymptotic properties of solutions”

Two problems in homogenization of porous media.

Jesús Ildefonso Díaz (1999)

Extracta Mathematicae

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The main goal of this work is to present two different problems arising in Fluid Dynamics of perforated domains or porous media. The first problem concerns the compressible flow of an ideal gas through a porous media and our goal is the mathematical derivation of Darcy's law. This is relevant in oil reservoirs, agriculture, soil infiltration, etc. The second problem deals with the incompressible flow of a fluid reacting with the exterior of many packed solid particles. This is related...

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

Takayuki Kobayashi, Wojciech Zajączkowski (1999)

Applicationes Mathematicae

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Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ 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 × + ) and the density belongs to H 1 + α , 1 / 2 + α / 2 ( Ω × + ) , α ∈ (1/2,1).