Displaying similar documents to “Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid”

Almost global solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid

Piotr Kacprzyk (2004)

Applicationes Mathematicae

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Almost global in time existence of solutions for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surfaced is proved. In the exterior domain we have an electromagnetic field which is generated by some currents which are located on a fixed boundary. We prove that a solution exists for t ∈ (0,T), where T > 0 is large if the data are small.

Global free boundary problem for incompressible magnetohydrodynamics

Piotr Kacprzyk

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We consider the motion of incompressible mhd in a domain bounded a free surface. In the external domain there exists an electromagnetic field generated by some currents which keeps the mhd flow in the bounded domain. On the free surface transmission conditions for the electromagnetic fields are imposed. For sufficiently small initial velocity and vanishing external force the global existence is proved. The L₂-approach is used. This helps us to treat the transmission conditions. ...

Local free boundary problem for incompressible magnetohydrodynamics

Piotr Kacprzyk

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We consider the motion of an incompressible magnetohydrodynamic (mhd) fluid in a domain bounded by a free surface. In the external domain there exists an electromagnetic field generated by some currents which keeps the mhd flow in the bounded domain. Then on the free surface transmission conditions for electromagnetic fields are imposed. In this paper we prove existence of local regular solutions by the method of successive approximations. The L₂ approach is used. This helps us to treat...

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...

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

Piotr Kacprzyk (2003)

Applicationes Mathematicae

Similarity:

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...

About the decay of surface waves on viscous fluids without surface tension

Gerhard Ströhmer (2003)

Banach Center Publications

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We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.

On some free boundary problems for Navier-Stokes equations

Ewa Zadrzyńska (2005)

Banach Center Publications

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In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.

On some inequalities for solutions of equations describing the motion of a viscous compressible heat-conducting capillary fluid bounded by a free surface

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2001)

Applicationes Mathematicae

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We derive inequalities for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. The inequalities are crucial in proving the global existence of solutions belonging to certain anisotropic Sobolev-Slobodetskii space and close to an equilibrium state.