论文标题
全球稳定的爆炸轮廓，用于所有维度的超临界波图
Globally stable blowup profile for supercritical wave maps in all dimensions
论文作者
论文摘要
我们考虑从$（1+d）$ - 尺寸Minkowski空间到$ d $ -sphere的波浪图。从Bizoń和Biernat \ cite {bizbie15}的工作中知道，在能量危机的情况下，即对于$ d \ geq 3 $，该模型承认了一种封闭形式的固定自我相似的爆炸解决方案。我们表明，对于所有$ d \ geq 3 $，此爆炸配置文件在全球范围内稳定，从而验证了有关该模型的通用大型数据爆炸行为，从而在\ cite {bizbie15}中提出的刺激性版本。为了实现这一目标，我们基于在整个空间上构成的相似性变量$ \ mathbb {r}^d $开发了一种新颖的稳定分析方法。结果，我们绘制了一个通用路线图，用于在径向案例中针对非线性波方程的自相似爆炸轮廓的空间全球稳定性$ d \ geq 3 $。
We consider wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere. It is known from the work of Bizoń and Biernat \cite{BizBie15} that in the energy-supercritical case, i.e., for $d \geq 3$, this model admits a closed-form corotational self-similar blowup solution. We show that this blowup profile is globally nonlinearly stable for all $d \geq 3$, thereby verifying a perturbative version of the conjecture posed in \cite{BizBie15} about the generic large data blowup behavior for this model. To accomplish this, we develop a novel stability analysis approach based on similarity variables posed on the whole space $\mathbb{R}^d$. As a result, we draw a general road map for studying spatially global stability of self-similar blowup profiles for nonlinear wave equations in the radial case for arbitrary dimension $d \geq 3$.
