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  Outgoing modal solutions for Galbrun's equation in helioseismology

Barucq, H., Faucher, F., Fournier, D., Gizon, L., & Pham, H. (2021). Outgoing modal solutions for Galbrun's equation in helioseismology. Journal of Differential Equations, 286, 494-530. doi:10.1016/j.jde.2021.03.031.

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Genre: Journal Article

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 Creators:
Barucq, Hélène, Author
Faucher, Florian, Author
Fournier, Damien1, Author              
Gizon, Laurent1, Author              
Pham, Ha, Author
Affiliations:
1Department Solar and Stellar Interiors, Max Planck Institute for Solar System Research, Max Planck Society, ou_1832287              

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Free keywords: Modal outgoing Green's kernel Galbrun's equation Helioseismology Indicial analysis Long-range scattering
 Abstract: We construct modal outgoing Green's kernels for the simplified Galbrun's equation under spherical symmetry, in the context of helioseismology. The coefficients of the equation are C2 functions representing the solar interior model S, complemented with an isothermal atmospheric model. We solve the equation in vectorial spherical harmonics basis to obtain modal equations for the different components of the unknown wave motions. These equations are then decoupled and written in Schrödinger form, whose coefficients are shown to be C2 apart from at most two regular singular points, and to decay like a Coulomb potential at infinity. These properties allow us to construct an outgoing Green's kernel for each spherical mode. We also compute asymptotic expansions of coefficients up to order r-3 as r tends to infinity, and show numerically that their accuracy is improved by including the contribution from the gravity although this term is of order r-3.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1016/j.jde.2021.03.031
 Degree: -

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Title: Journal of Differential Equations
Source Genre: Journal
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Publ. Info: Amsterdam : Academic Press
Pages: - Volume / Issue: 286 Sequence Number: - Start / End Page: 494 - 530 Identifier: ISSN: 0022-0396
CoNE: https://pure.mpg.de/cone/journals/resource/954922645033