三维拟线性波方程的小初值光滑解

Small Data Solutions of 3-D Quasilinear Wave Equations

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.

For the 3-D quasilinear wave equation 3∑（i,j=0） gij（u） iju=0, a global existence result has been shown by H. Lindblad. This paper deals with this 3-D quasilinear wave equation 3∑（i,j=0） gij（u） iju=（ 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.