On almost global existence and local well posedness for some 3-D quasi-linear wave equations
On almost global existence and local well posedness for some 3-D quasi-linear wave equations
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DOI：
10.57262/ade/1355703087
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发表时间：
2010-04
影响因子：
1.4
通讯作者：
K. Hidano;Chengbo Wang;K. Yokoyama
中科院分区：
文献类型：
--
作者：
K. Hidano;Chengbo Wang;K. Yokoyama
研究了一类拟线性波动方程的Cauchy问题。变系数波动方程的时空L^2估计在这方面起着核心作用。假设径向对称，我们建立了强解的几乎整体存在性，每个小的初始数据在$H^2 \times H^1$。我们还证明了初值问题是局部适定的。
We study the Cauchy problem for a quasilinear wave equation with low-regularity data. A space-time $L^2$ estimate for the variable coefficient wave equation plays a central role for this purpose. Assuming radial symmetry, we establish the almost global existence of a strong solution for every small initial data in $H^2 \times H^1$. We also show that the initial value problem is locally well-posed.