Global Stability for Nonlinear Wave Equations Satisfying a Generalized Null Condition

被引:0
作者
Anderson, John [1 ]
Zbarsky, Samuel [1 ]
机构
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
基金
美国国家科学基金会;
关键词
VECTOR FIELD METHOD; SPACE-TIME; BLOW-UP; EXISTENCE; DECAY;
D O I
10.1007/s00205-024-02025-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove global stability for nonlinear wave equations satisfying a generalized null condition. The generalized null condition is made to allow for null forms whose coefficients have bounded Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>k$$\end{document} norms. We prove both the pointwise decay and improved decay of good derivatives using bilinear energy estimates and duality arguments. Combining this strategy with the rp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r<^>p$$\end{document} estimates of Dafermos-Rodnianski then allows us to prove the global stability. The proof requires analyzing the geometry of intersecting null hypersurfaces adapted to solutions of wave equations.
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页数:62
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