| 三维拟线性波方程的小初值光滑解 |
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| 引用本文： | 刘颖博. 三维拟线性波方程的小初值光滑解[J]. 数学年刊A辑(中文版), 2018, 39(2): 127-144 |
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| 作者姓名： | 刘颖博 |
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| 作者单位： | 中国药科大学理学院 |
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| 基金项目： | 本文受到国家自然科学基金(No.11371189)的资助. |
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| 摘 要： | 对三维小初值拟线性波方程3∑(i,j=0)g~(ij)(u)■_(ij)u=0,H.Lindblad证明了它有整体光滑解.本文考虑如下带有小初值的拟线性波方程3∑(i,j=0)g~(ij)(u)■_(ij)u=(■u)~3,通过得到低阶导数的衰减估计和高阶导数的能量估计,由连续论证法证明了这个方程也存在整体光滑解.
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| 关 键 词： | 整体解 零标架 加权能量估计 连续论证法 |
| 收稿时间： | 2016-07-24 |
| 修稿时间： | 2017-05-06 |
Small Data Solutions of 3-D Quasilinear Wave Equations |
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| LIU Yingbo. Small Data Solutions of 3-D Quasilinear Wave Equations[J]. Chinese Annals of Mathematics, 2018, 39(2): 127-144 |
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| Authors: | LIU Yingbo |
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| Affiliation: | School of Science, China Pharmaceutical University,Nanjing 210009, China. |
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| Abstract: | For the 3-D quasilinear wave equation $sumlimits_{i,j=0}^3g^{ij}(u)p_{ij}u=0$,a global existence result has been shown by H. Lindblad.This paper deals with this 3-D quasilinear wave equation$sumlimits_{i,j=0}^3g^{ij}(u)p_{ij} u=(p u)^3$ with small initialdata. Through deriving decay estimates of low derivativesand energy estimates for high derivatives, combined withknown weighted energy inequality, a global existencesolution is also established by continuous induction. |
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| Keywords: | Global existence Null frame Weighted energy estimate Continuous induction |
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