In this paper we study the blow-up analysis for some mean field equation on point vortices which is derived by C. Neri under a stochastic assumption. In particular, we derive some estimate which is the asymptotic behavior of blow-up solutions near the blow-up points. To obtain this result we shall employ the new scaling argument for blow-up solutions of Neri's mean field equation. Moreover, we also study the power type elliptic equation in higher dimension case related to mean field equation and derive such estimate.

中文翻译：

---

二维湍流中 Neri 平均场方程的爆破分析

在本文中，我们研究了 C. Neri 在随机假设下推导出的点涡平均场方程的爆破分析。特别是，我们得出了一些估计，即在爆破点附近爆破解的渐近行为。为了获得这个结果，我们将采用新的缩放参数来解决 Neri 平均场方程的爆炸解。此外，我们还研究了与平均场方程相关的高维情况下的幂型椭圆方程，并得出了这种估计。