具有径向对称数据的Reynsey猜想
The Glassey conjecture with radially symmetric data
摘要：
本文在径向情形下证明了关于空间维数为任意维数的非线性波动方程$\Box u=|\nabla u|^p$的全局小解存在的临界指数由$p_c=1+\frac{2}{n-1}$给出.此外，我们能够证明的存在性结果与低正则性假设的初始数据和扩展的解决方案的尖锐的生命周期。主要思想是利用迹估计和KSS型估计。
英文摘要：
In this paper, we verify the Glassey conjecture in the radial case for all spatial dimensions, which states that, for the nonlinear wave equations of the form $\Box u=|\nabla u|^p$, the critical exponent to admit global small solutions is given by $p_c=1+\frac{2}{n-1}$. Moreover, we are able to prove the existence results with low regularity assumption on the initial data and extend the solutions to the sharp lifespan. The main idea is to exploit the trace estimates and KSS type estimates.
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