Magnetic hydrodynamics equations in movingboundaries

Hiroshi Inoue

doi:10.3934/proc.2005.2005.397

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2005, Volume 2005: 397-402. Doi: 10.3934/proc.2005.2005.397 open access

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Magnetic hydrodynamics equations in movingboundaries

Hiroshi Inoue^1,

1.
Ashikaga Institute of Technology, 268-1 Omae Ashikaga, Tochigi, 326-8558

Received: August 31, 2004

Revised: April 30, 2005

Published: August 2005

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Abstract

We show the existence and uniqueness of the strong solutions of the zero Dirichlet problems of the coupled Navier-Stokes equations which govern the incompressible magnetic fluid. We derive the existence of a unique strong solution for suitable initial conditions which depend on the space dimensions. The proofs have been shown to apply the contraction mapping theorem by using the theory of the sub-differential operators.

Keywords:

Strong Solution,
Coupled Navier-Stokes equation.

Mathematics Subject Classification: Primary: 76W05; Secondary: 35K70.

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