The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher ℓdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ell $$end{document}-Modes of Linear Waves on a Schwarzschild Background

Kehrberger Leonhard M. A.

首页> 外文期刊>Annals of PDE. (Partial Differential Equations) >The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher ℓdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ell $$end{document}-Modes of Linear Waves on a Schwarzschild Background

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The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher ℓdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ell $$end{document}-Modes of Linear Waves on a Schwarzschild Background

机译：The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher ℓdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ell $$end{document}-Modes of Linear Waves on a Schwarzschild Background

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Abstract In this paper, we derive the early-time asymptotics for fixed-frequency solutions ϕℓdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$phi _ell $$end{document} to the wave equation □gϕℓ=0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Box _g phi _ell =0$$end{document} on a fixed Schwarzschild background (M>0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$M>0$$end{document}) arising from the no incoming radiation condition on I-documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${mathscr {I}}^-$$end{document} and polynomially decaying data, rϕℓ∼t-1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$rphi _ell sim t^{-1}$$end{document} as t→-∞documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$trightarrow -infty $$end{document}, on either a timelike boundary of constant area radius r>2Mdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$r>2M$$end{document}(I) or an ingoing null hypersurface (II). In case (I), we show that the asymptotic expansion of ∂v(rϕℓ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$partial _v(rphi _ell )$$end{document} along outgoing null hypersurfaces near spacelike infinity i0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$i^0$$end{document} contains logarithmic terms at order r-3-ℓlogrdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$r^{-3-ell }log r$$end{document}. In contrast, in case (II), we obtain that the asymptotic expansion of ∂v(rϕℓ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$partial _v(rphi _ell )$$end{document} near spacelike infinity i0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$i^0$$end{document} contains logarithmic terms already at order r-3logrdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} se

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《Annals of PDE. (Partial Differential Equations)》 |2022年第2期|共5页
作者
Kehrberger Leonhard M. A.;
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University of Cambridge;

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正文语种英语
中图分类偏微分方程;
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Price’s law; Asymptotics; Logarithmic Asymptotics; Early-time asymptotics; Scattering constructions; Boundary value problem; Peeling;

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