Displaying similar documents to “Multiphase free boundary problem for the equations of motion of general fluids”

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.

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. ...

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 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...