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Title: Applications of parabolic Dirac operators to the instationary viscous MHD equations on conformally flat manifolds
Author: Cerejeiras, Paula
Kähler, Uwe
Kraußhar, Sören R.
Keywords: Quaternionic integral operator calculus
Instationary incompressible viscous magnetohydrodynamics equations
Parabolic Dirac operators
Fundamental solutions
Conformally flat manifolds
PDE on spin manifolds
Issue Date: 2019
Publisher: Birkhäuser
Abstract: In this paper we apply classical and recent techniques from quaternionic analysis using parabolic Dirac type operators and related Teodorescu and Cauchy-Bitzadse type operators to set up some analytic representation formulas for the solutions to the time dependent incompressible viscous magnetohydrodynamic equations on some conformally flat manifolds, such as cylinders and tori associated with different spinor bundles. Also in this context a special variant of hypercomplex Eisenstein series related to the parabolic Dirac operator serve as kernel functions.
Peer review: yes
DOI: 10.1007/978-3-030-23854-4_8
ISBN: 978-3-030-23853-7
Appears in Collections:CIDMA - Capítulo de livro
DMat - Capítulo de livro
CHAG - Capítulo de livro

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