Displaying similar documents to “On the stationary motion of compressible viscous fluids”

On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

Piotr Mucha, Wojciech Zajączkowski (2000)

Applicationes Mathematicae

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The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that u ∈ W r 2 , 1 ( Ω ˜ T ) with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the L p -approach the Lagrangian coordinates must be used....

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 ⊂ 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).