IF 2.6 1区 数学 Q1 MATHEMATICS, APPLIED
André Guerra, Rita Teixeira da Costa
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引用次数: 0

摘要

1989 年,伯内特猜想,在适当的假设条件下,爱因斯坦真空方程高度振荡解的极限是爱因斯坦无质量弗拉索夫系统的解。最近,Huneau-Luk(Ann Sci l'ENS,2024)在 U(1)-symmetry 和椭圆规中证明了这一猜想。他们还要求控制高达四阶的度量分量导数。在本文中,我们给出了一个更强结果的简化证明,并本着伯内特最初猜想的精神,取消了对高阶导数的控制要求。我们的方法也适用于一般波映射方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Oscillations in Wave Map Systems and Homogenization of the Einstein Equations in Symmetry

In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein–massless Vlasov system. In a recent breakthrough, Huneau–Luk (Ann Sci l’ENS, 2024) gave a proof of the conjecture in U(1)-symmetry and elliptic gauge. They also require control on up to fourth order derivatives of the metric components. In this paper, we give a streamlined proof of a stronger result and, in the spirit of Burnett’s original conjecture, we remove the need for control on higher derivatives. Our methods also apply to general wave map equations.

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来源期刊
CiteScore
5.10
自引率
8.00%
发文量
98
审稿时长
4-8 weeks
期刊介绍: The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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