论文标题
一般非碰撞对称空间上的波动方程
Wave equation on general noncompact symmetric spaces
论文作者
论文摘要
我们在不正确的对称空间上建立了尖锐的内核估计和分散性能。这是通过将固定相法和Hadamard参数（尤其是引入微妙的频谱分解）结合起来来实现的，这使我们能够克服高级分析中的众所周知的难度，即Plancherel密度不是通常的差异符号。结果，我们推断出大型可允许对家庭的Strichartz不等式，并证明了相应的半线性方程的全球适应性结果，具有低规律性数据，如双曲线空间。
We establish sharp pointwise kernel estimates and dispersive properties for the wave equation on noncompact symmetric spaces of general rank. This is achieved by combining the stationary phase method and the Hadamard parametrix, and in particular, by introducing a subtle spectral decomposition, which allows us to overcome a well-known difficulty in higher rank analysis, namely the fact that the Plancherel density is not a differential symbol in general. As consequences, we deduce the Strichartz inequality for a large family of admissible pairs and prove global well-posedness results for the corresponding semilinear equation with low regularity data as on hyperbolic spaces.
