论文标题
关于吉布斯的措施和外部型孤子图
On Gibbs measures and topological solitons of exterior equivariant wave maps
论文作者
论文摘要
我们考虑$ k $ - equivariant波映射来自外部空间域$ \ mathbb {r}^3 \ backslash b（0,1）$的$ \ mathbb {s}^3 $。该模型具有无限的许多拓扑词汇$ q_ {n，k} $，它们由其拓扑度$ n \ in \ mathbb {z} $索引。对于\ Mathbb {z} $和$ k \ geq 1 $的每个$ n \，我们证明了$ q_ {n，k} $的Gibbs度量的存在和不变性。作为推论，我们获得了孤子分辨率因随机初始数据而失败。由于Soliton分辨率在能量空间中以初始数据而闻名，因此这揭示了确定性和概率观点之间的鲜明对比。
We consider $k$-equivariant wave maps from the exterior spatial domain $\mathbb{R}^3\backslash B(0,1)$ into the target $\mathbb{S}^3$. This model has infinitely many topological solitons $Q_{n,k}$, which are indexed by their topological degree $n\in \mathbb{Z}$. For each $n\in \mathbb{Z}$ and $k\geq 1$, we prove the existence and invariance of a Gibbs measure supported on the homotopy class of $Q_{n,k}$. As a corollary, we obtain that soliton resolution fails for random initial data. Since soliton resolution is known for initial data in the energy space, this reveals a sharp contrast between deterministic and probabilistic perspectives.
