Global Well-posedness for the Logarithmically Energy-Supercritical Nonlinear Wave Equation with Partial Symmetry
Global Well-posedness for the Logarithmically Energy-Supercritical Nonlinear Wave Equation with Partial Symmetry
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DOI：
10.1093/imrn/rnz019
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发表时间：
2018-07
影响因子：
1
通讯作者：
Aynur Bulut;B. Dodson
中科院分区：
文献类型：
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作者：
Aynur Bulut;B. Dodson
假设初始数据满足部分对称条件，我们建立了对数能量超临界非线性波动方程的全局适定性和散射结果。这些结果概括并扩展了Tao 在径向对称环境中的工作。所涉及的技术包括 Morawetz 和 Strichartz 估计的加权版本，权重适应部分对称假设。在附录中，我们为能源关键问题建立了相应的定量结果。
We establish global well-posedness and scattering results for the logarithmically energy-supercritical nonlinear wave equation, under the assumption that the initial data satisfies a partial symmetry condition. These results generalize and extend work of Tao in the radially symmetric setting. The techniques involved include weighted versions of Morawetz and Strichartz estimates, with weights adapted to the partial symmetry assumptions. In an appendix, we establish a corresponding quantitative result for the energy-critical problem.