%0 Journal Article
%T 三维拟线性波方程的小初值光滑解<br>Small Data Solutions of 3-D Quasilinear Wave Equations
%A 刘颖博
%J 数学年刊（A辑）
%D 2018
%R 10.16205/j.cnki.cama.2018.0012
%X 对三维小初值拟线性波方程$\sum\limits_{i,j=0}^3g^{ij}( u)\p_{ij}u=0$, 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$\sum\limits_{i,j=0}^3g^{ij}(u)\p_{ij} u=(\p u)^3$, 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.<br>For the 3-D quasilinear wave equation $\sum\limits_{i,j=0}^3g^{ij}(u)\p_{ij}u=0$, a global existence result has been shown by H. Lindblad. This paper deals with this 3-D quasilinear wave equation $\sum\limits_{i,j=0}^3g^{ij}(u)\p_{ij} u=(\p u)^3$ with small initial data. Through deriving decay estimates of low derivatives and energy estimates for high derivatives, combined with known weighted energy inequality, a global existence solution is also established by continuous induction.
%K 整体解
%K 零标架
%K 加权能量估计
%K 连续论证法&lt
%K br&gt
%K Global existence
%K Null frame
%K Weighted energy estimate
%K Continuous induction
%U http://www.camath.fudan.edu.cn/camacn/ch/reader/view_abstract.aspx?file_no=39A202&flag=1