基态阈值下能量临界 Zakharov 系统的全局适定性
偏微分方程分析
2023-10-10 v4
摘要
考虑了能量临界维数 下 Zakharov 系统的柯西问题。我们证明：对于任意能量与波质量低于基态阈值的初值，在全（非径向）能量空间中均成立全局适定性。该结果基于带势的薛定谔方程的 Strichartz 估计。更确切地说，证明了对于任意满足质量低于基态约束的自由波方程解的势，Strichartz 估计一致成立。关键的新要素是针对非齐次薛定谔方程、其强迫项位于对偶端点 Strichartz 空间中的解的双线性（伴随）傅里叶限制估计。
引用
@article{arxiv.2005.09932,
title = {Global wellposedness for the energy-critical Zakharov system below the ground state},
author = {Timothy Candy and Sebastian Herr and Kenji Nakanishi},
journal= {arXiv preprint arXiv:2005.09932},
year = {2023}
}
备注
Partly, the notation in Section 2 is adopted from arXiv:1912.05820. v2: references fixed, further minor corrections. v3: Minor change of Theorem 4.1 and its proof, which includes low frequeny cases now. v4: fixed references to [7]