On the Global Behavior of Weak Null Quasilinear Wave Equations

被引：15

作者：

Deng, Yu ^{[1
]}

Pusateri, Fabio ^{[2
,3
]}

机构：

[1] Courant Inst Math Sci, New York, NY USA

[2] Princeton Univ, Princeton, NJ 08544 USA

[3] Univ Toronto, 40 St George St,Room 6218, Toronto, ON M5S 2E4, Canada

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2020年 / 73卷 / 05期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

EINSTEIN VACUUM EQUATIONS; ASYMPTOTIC-BEHAVIOR; WATER-WAVES; NONLINEAR SCHRODINGER; SPACE-TIME; BLOW-UP; SYSTEMS; SCATTERING; EXISTENCE;

D O I：

10.1002/cpa.21881

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a subclass of those quasilinear wave equations in 3 + 1 space-time dimensions that satisfy the "weak null condition" as defined by Lindblad and Rodnianski , and study the large-time behavior of solutions to the Cauchy problem. The prototype for the class of equations considered is - partial differential t2u+1+u Delta u=0. Global solutions for such equations have been constructed by Lindblad and Alinhac. Our main results are the derivation of a precise asymptotic system with good error bounds, and a detailed description of the behavior of solutions close to the light cone, including the blowup at infinity. (c) 2019 Wiley Periodicals, Inc.

引用

页码：1035 / 1099

页数：65

共 44 条

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Alazard T, 2015, ANN SCI ECOLE NORM S, V48, P1149

[2]

Alinhac S, 2003, ASTERISQUE, P1

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