Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in $\dot{H}^{s} \times \dot{H}^{s - 1}$, $s> \frac{1}{2}$
Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in $\dot{H}^{s} \times \dot{H}^{s - 1}$, $s> \frac{1}{2}$
复制标题
$dot{H}^{s} imes dot{H}^{s - 1}$, $s> 中径向初始数据的三维散焦三次非线性波动方程的全局适定性
DOI：
10.1093/imrn/rnx323
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发表时间：
2018
影响因子：
1
通讯作者：
Dodson, Benjamin
中科院分区：
文献类型：
--
作者：
Dodson, Benjamin
本文研究三维空间中具有径向初值的三次非线性离焦波动方程。关键的空间是。我们证明了，如果初始数据是径向的，并且对于某些位于，那么三次初值问题是全局适定的。证明利用了I-方法，长时间的Escherichartz估计，和当地的能量衰减。此方法与中使用的方法非常相似。
In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is. We show that if the initial data is radial and lies infor some, then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in .