论文标题
关于真实行的De Gregorio模型的自相似的有限时间爆炸
On self-similar finite-time blowups of the De Gregorio model on the real line
论文作者
论文摘要
我们表明，真实线上的De Gregorio模型承认，许多紧凑的支持，相似的解决方案在重新恢复中与众不同，并且会在有限的时间内爆炸。这些自相似的解决方案分为两个类别：基本类和通用类。基本类别由无数的无限解决方案组成，这些解决方案是一个自动辅助紧凑型操作员的本征函数。特别是，领先的征函数与最近通过数值方法获得的De Gregorio模型的有限时间奇异性解相吻合。通用类由更复杂的解决方案组成，可以通过解决与同一紧凑型操作员相关的非线性特征值问题获得。
We show that the De Gregorio model on the real line admits infinitely many compactly supported, self-similar solutions that are distinct under rescaling and will blow up in finite time. These self-similar solutions fall into two classes: the basic class and the general class. The basic class consists of countably infinite solutions that are eigenfunctions of a self-adjoint compact operator. In particular, the leading eigenfunction coincides with the finite-time singularity solution of the De Gregorio model recently obtained by numerical approaches. The general class consists of more complicated solutions that can be obtained by solving nonlinear eigenvalue problems associated with the same compact operator.
