SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2158-2178, January 2020.
We investigate a system of nonlocal transport equations in one spatial dimension. The system can be regarded as a model for the three-dimensional Euler equations in the hyperbolic flow scenario. We construct blowup solutions with control over the vorticity up to the blowup time. For a wide class of initial data, we determine power-law bounds for the blowup profile with an exact exponent derived from a stationary singular solution of the system.

中文翻译：

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具有涡旋伸展性的非局部演化方程组的奇异解

SIAM数学分析杂志，第52卷，第2期，第2158-2178页，2020年1月。
我们研究了在一个空间维度上的非局部输运方程组。该系统可以看作是双曲流情况下三维欧拉方程的模型。我们构造爆破解决方案，并控制爆破时间之前的涡度。对于一大类初始数据，我们使用从系统的固定奇异解中得出的精确指数来确定爆炸分布的幂律边界。