Propagation of polarization sets for systems of generalized transverse type and for systems of MHD type

by Rayhana Darwich
Doctoral thesis
Date of Examination:2023-05-02
Date of issue:2023-06-16
Advisor:Prof. Dr. Ingo Witt
Referee:Prof. Dr. Dorothea Bahns
Referee:Dr. Christian Jaeh
Persistent Address: http://dx.doi.org/10.53846/goediss-9929

 

 

Files in this item

Name:PhD thesis (03.June.2023).pdf
Size:1.25Mb
Format:PDF
Description:PhD Thesis

The following license files are associated with this item:

Abstract

English

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 thesis, we consider the case of more than two intersecting characteristic hypersurfaces that are interesting 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 transverse type. Furthermore, we give an application to the MHD equations.
Keywords: Polarization sets; wavefront sets; systems of transverse type; systems of uniaxial type; systems of generalized transverse type; systems of MHD type; magnetohydrodynamics; ideal MHD equations; pseudodifferential operators; systems of real principal type; propagation of polarization sets; microlocal analysis
 
Statistik