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Displaying similar documents to “Global free boundary problem for incompressible magnetohydrodynamics”

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...

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.

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.

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.

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...

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

Piotr Kacprzyk (2004)

Applicationes Mathematicae

Similarity:

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...

Numerical simulation of free-surface flows with surface tension

Sváček, Petr

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This paper focuses on the mathematical modelling and the numerical approximation of the flow of two immiscible incompressible fluids. The surface tension effects are taken into account and mixed boundary conditions are used. The weak formulation is introduced, discretized in time, and the finite element method is applied. The free surface motion is treated with the aid of the level set method. The numerical results are shown.