论文标题
完全相似的de Gregorio方程式的自相似
Exactly self-similar blow-up of the generalized De Gregorio equation
论文作者
论文摘要
We study exactly self-similar blow-up profiles fot the generalized De Gregorio model for the three-dimensional Euler equation: $w_t + auw_x = u_xw, \quad u_x = Hw$ We show that for any $α\in (0, 1)$ such that $|aα|$ is sufficiently small, there is an exactly self-similar $C^α$ solution that blows up in finite time.通过删除\ Mathbb z $中的限制$ 1/α\和\ cite {el-ghma，chhohu}，这同时改善了\ cite {elje}的结果，该限制仅处理非属性自我仿制的爆炸。
We study exactly self-similar blow-up profiles fot the generalized De Gregorio model for the three-dimensional Euler equation: $w_t + auw_x = u_xw, \quad u_x = Hw$ We show that for any $α\in (0, 1)$ such that $|aα|$ is sufficiently small, there is an exactly self-similar $C^α$ solution that blows up in finite time. This simultaneously improves on the result in \cite{ElJe} by removing the restriction $1/α\in \mathbb Z$ and \cite{El-GhMa,ChHoHu}, which only deals with asymptotically self-similar blow-ups.
