Displaying similar documents to “On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary”

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).

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 nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary

Ewa Zadrzyńska (1999)

Applicationes Mathematicae

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The motion of a fixed mass of a viscous compressible heat conducting capillary fluid is examined. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global-in-time solution which is close to the constant state for any moment of time. Moreover, we present an analogous result for the case of a barotropic viscous compressible fluid.

Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic compressible fluid

Piotr Kacprzyk (2004)

Applicationes Mathematicae

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Local existence of solutions for the equations describing the motion of a magnetohydrodynamic compressible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linearized equations is proved, next by the method of successive aproximations local existence to the nonlinear...

Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid

Piotr Kacprzyk (2005)

Banach Center Publications

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Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.

Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid

Piotr Kacprzyk (2003)

Applicationes Mathematicae

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Local existence of solutions is proved for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surface. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linarized equations is proved; next by the method of successive aproximations the local existence is shown for the...