On the Global Behavior of Weak Null Quasilinear Wave Equations

IF 3.5 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2019-12-24 DOI:10.1002/cpa.21881

Yu Deng, Fabio Pusateri

引用次数: 22

Abstract

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 . 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. © 2019 Wiley Periodicals, Inc.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.