Geodesic
Propagation of polarization sets for systems of MHD type
Documenta mathematica, Tome 29 (2024) no. 4, pp. 921-957

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Polarization sets were introduced by Dencker (1982) as a refinement of wavefront sets to the vector-valued case. He also clarified the propagation of polarization sets when the characteristic variety of the pseudodifferential system under study consists of two hypersurfaces intersecting tangentially (1992), or transversally (1995). In this paper, we consider the case of more than two intersecting characteristic hypersurfaces that are intersecting transversally (and we give a note on the tangential case). Mainly, we consider two types of systems which we name “systems of generalized transverse type” and “systems of MHD type”, and we show that we can get a result for the propagation of polarization set similar to Dencker’s result for systems of transversal type. Furthermore, we give an application to the MHD equations.
DOI : 10.4171/dm/966
Classification : 58J47, 35S05, 58J40, 76W05
Mots-clés : propagation of polarization sets, systems of generalized transverse type, systems of MHD type, applications in magnetohydrodynamics 
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     author = {Rayhana Darwich},
     title = {Propagation of polarization sets for systems of {MHD} type},
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     year = {2024},
     doi = {10.4171/dm/966},
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Rayhana Darwich. Propagation of polarization sets for systems of MHD type. Documenta mathematica, Tome 29 (2024) no. 4, pp. 921-957. doi: 10.4171/dm/966

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