Small solutions to semi-linear wave equations with radial data of critical regularity
Small solutions to semi-linear wave equations with radial data of critical regularity
复制标题
具有临界正则性径向数据的半线性波动方程的小解
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
K. Hidano
中科院分区：
文献类型：
--
作者：
K. Hidano
研究了具有临界正则性径向对称数据的半线性波动方程小解的整体存在性问题。在径向对称条件下，我们主要研究非线性项的幂比共形项的幂小的情况。我们的结果涵盖的情况下，权力是严格大于John-Bossey指数在两个或三个空间维度。在高维情况下，它适用于幂严格大于L2-临界指数的方程。因此，主要定理是对Lindblad和Sogge先前结果的改进。在我们的证明中的新成分是一个有效的使用径向对称解的非齐次波动方程的一些加权估计。
This paper investigates the problem of global existence of small solutions to semi-linear wave equations with radially symmetric data of critical regularity. Under radial symmetry we focus on the case where the power of nonlinear term is somewhat smaller than the conformal power. Our result covers the case where the power is strictly larger than the John-Glassey exponent in two or three space dimensions. In higher dimension it applies to the equation whose power is strictly larger than the L2-critical exponent. The main theorem is therefore an improvement over a previous result due to Lindblad and Sogge. The new ingredient in our proof is an effective use of some weighted estimates of radially symmetric solutions to inhomogeneous wave equations.