ASYMPTOTIC ANALYSIS OF EXTENDED MAGNETOHYDRODYNAMICS
Résumé
The derivation of a reduced eXtended MagnetoHydroDynamic (XMHD) model for fusion plasma is formulated as a singular limit of a hyperbolic-parabolic system implying a large parameter. It is proven that the solutions to the barotropic XMHD system converge to those of a well-posed corresponding reduced model, thereby providing a rigorous justification for its use as a modulation equation for both theoretical and numerical studies. Our analysis involves many new aspects in comparison with well-known results about incompressible limits, including the XMHD specificities and, due to the presence of anisotropy, the use of a pseudo-differential symmetrizer whose symbol involves singularities along a line.
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