Global stability of solutions to nonlinear wave equations

被引：13

作者：

Yang, Shiwu ^{[1
]}

机构：

[1] Univ Cambridge, Ctr Math Sci, DPMMS, Cambridge CB3 0WA, England

来源：

SELECTA MATHEMATICA-NEW SERIES | 2015年 / 21卷 / 03期

关键词：

Null condition; Semilinear wave equation; Global stability; 2 SPACE DIMENSIONS; GENERAL-RELATIVITY; EXTERIOR DOMAINS; MULTIPLE SPEEDS; MINKOWSKI SPACE; EXISTENCE; SYSTEMS; DECAY; TIME; 3D;

D O I：

10.1007/s00029-014-0165-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution, which guarantees stability. Our stability result can be reduced to a small data global existence result for a class of semilinear wave equations with linear terms , and quadratic terms where the functions , , decay rather weakly and the constants satisfy the null condition. We show the small data global existence result by using the new approach developed by Dafermos-Rodnianski. In particular, we prove the global stability result under weaker assumptions than those imposed by Alinhac (Indiana Univ Math J 58(6):2543-2574, 2009).

引用

页码：833 / 881

页数：49