Outgoing modal solutions for Galbrun's equation in helioseismology

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:286

Article

Barucq, Helene¹  Faucher, Florian²  Fournier, Damien³  Gizon, Laurent³  Pham, Ha¹ 

[1] CNRS, E2S UPPA, Inria Project Team Mag 3D, Pau, France

[2] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] Max Planck Inst Sonnensystemforsch, Justus Von Liebig Weg 3, D-37077 Gottingen, Germany

关键词: Modal outgoing Green's kernel;    Galbrun's equation;    Helioseismology;    Indicial analysis;    Long-range scattering;   

DOI  :  10.1016/j.jde.2021.03.031

来源: Elsevier

【 摘 要 】

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 C-2 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 Schrodinger form, whose coefficients are shown to be C-2 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). (C) 2021 The Authors. Published by Elsevier Inc.

【 授权许可】

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