On the Well-posedness of Magnetohydrodynamics Equations for Incompressible Electrically-Conducting Fluids

F. Lam

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arXiv · 1401.2029

On the Well-posedness of Magnetohydrodynamics Equations for Incompressible Electrically-Conducting Fluids

F. Lam

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Abstract

It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled magnetic-vortical field has the characters of turbulence, if the initial data exceed certain size. In particular, if a strong magnetic force dominates the flow evolution, the current density possesses a cubic non-linearity. The solution of the non-linear problem has been constructed and has been expressed as an infinite series.

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F. Lam. 2014-01-09. On the Well-posedness of Magnetohydrodynamics Equations for Incompressible Electrically-Conducting Fluids. https://arxiv.org/abs/1401.2029

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