Unconditional well-posedness for the energy-critical nonlinear damped wave equation
Unconditional well-posedness for the energy-critical nonlinear damped wave equation
复制标题
能量临界非线性阻尼波动方程的无条件适定性
DOI：
10.1007/s00028-021-00744-9
复制
发表时间：
2021
影响因子：
1.4
通讯作者：
Wakasugi Yuta
中科院分区：
文献类型：
--
作者：
Inui Takahisa;Wakasugi Yuta
对于能量临界的非线性阻尼波方程，我们证明了其无条件适定性。无条件适定意味着局部适定和无条件唯一性。首先，我们给出了局部适定性和稳定性，它的表述将有助于研究全局动力学。其次，我们证明了无条件唯一性。由于这些问题似乎作为波动方程的直接摄动是不可解的，所以我们将Strichartz估计应用于包括波端点情况在内的阻尼波方程。
For the energy-critical nonlinear damped wave equation, we show the unconditional well-posedness. The unconditional well-posedness means local well-posedness and the unconditional uniqueness. First, we give the local well-posedness and stability, whose statement will be useful to investigate the global dynamics. At second, we show the unconditional uniqueness. Since these problems seem not to be solvable as a direct perturbation of the wave equation, we apply the Strichartz estimates for the damped wave equation including the wave endpoint case.