ASYMPTOTICS OF RADIATION FIELDS IN ASYMPTOTICALLY MINKOWSKI SPACE

被引：37

作者：

Baskin, Dean ^{[1
]}

Vasy, Andras ^{[2
]}

Wunsch, Jared ^{[1
]}

机构：

[1] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2015年 / 137卷 / 05期

基金：

美国国家科学基金会;

关键词：

SCATTERING-THEORY; WAVE-EQUATION; SYMBOLIC POTENTIALS; ORDER ZERO; PROPAGATION; MANIFOLDS; SINGULARITIES; RESOLVENT;

D O I：

10.1353/ajm.2015.0033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a non-trapping n-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation in all asymptotic regimes. The rates of decay seen in the asymptotic expansion are related to the resonances of a natural asymptotically hyperbolic problem on the "northern cap" of the compactification. For small perturbations of Minkowski space that fit into our framework, our asymptotic expansions yield a rate of decay that improves on the Klainerman-Sobolev estimates.

引用

页码：1293 / 1364

页数：72

共 26 条

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