An elementary proof of Strauss conjecture
An elementary proof of Strauss conjecture
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DOI：
10.1016/j.jfa.2014.05.020
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发表时间：
2014-09
影响因子：
1.7
通讯作者：
Ning-An Lai;Yi Zhou
中科院分区：
文献类型：
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作者：
Ning-An Lai;Yi Zhou
本文考虑高维半线性波动方程的Cauchy问题。首先利用在光锥上积分得到的Morawetz能量估计得到了解的加权L2 − L2估计，然后给出Georgiev等人的加权Morawetz估计的初等证明. [3]因此，施特劳斯猜想。我们还得到了一个变形的加权Eschhartz估计，并给出了半线性波动方程的寿命的尖锐估计。
In this paper, we consider the Cauchy problem for semilinear wave equation in high dimensions. First we use a Morawetz energy estimate which is obtained by integrating on the light cone to get a weighted L 2− L 2 estimate of the solution, and then give an elementary proof of the weighted Strichartz estimate in Georgiev et al.[3], hence the Strauss conjecture. We also obtain a variant of the weighted Strichartz estimates and give the sharp estimate of the lifespan for the semilinear wave equation with subcritical nonlinearity.