论文标题
爆炸动力学，用于平滑的模棱两可的解决方案至关重要的解决方案
Blowup dynamics for smooth equivariant solutions to energy critical Landau-Lifschitz flow
论文作者
论文摘要
在本文中，我们研究了能量关键的1-等级landau-lifschitz流量映射$ \ mathbb {r}^2 $ to $ \ mathbb {s}^2 $具有任意给定系数的$ρ_1\ in \ Mathbb {r} $，$ρ_2> 0 $ $ρ_1\。我们证明，存在一组平滑稳定的初始数据集，该集合任意接近地面状态，该数据生成了II型有限时间爆炸解决方案，并对相应的奇异性形成进行了精确描述。在我们的证明中，Schrödinger部分和热点在近似溶液的构建和混合能量/Morawetz功能中都起着重要作用。但是，爆炸速率与系数无关。
In this paper, we study the energy critical 1-equivariant Landau-Lifschitz flow mapping $\mathbb{R}^2$ to $\mathbb{S}^2$ with arbitrary given coefficients $ρ_1\in \mathbb{R}$, $ρ_2>0$. We prove that there exists a codimension one smooth well-localized set of initial data arbitrarily close to the ground state which generates type-II finite-time blowup solutions, and give a precise description of the corresponding singularity formation. In our proof, both the Schrödinger part and the heat part play important roles in the construction of approximate solutions and the mixed energy/Morawetz functional. However, the blowup rate is independent of the coefficients.
