We study the global existence of the singular nonlinear parabolic Anderson model equation on $2$-dimensional tours ${𝕋}^2$. The method is based on paracontrolled distribution and renormalization. After splitting the original nonlinear parabolic Anderson model equation into two simple equations, we prove the global well-posedness by some a priori estimates and smooth approximations. Furthermore, we prove the uniqueness of the solution by using classical energy estimates.

中文翻译：

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非线性广义抛物型安德森模型方程的全局适定性

我们研究了奇异非线性抛物线安德森模型方程的全局存在性$2$立体游${𝕋}^2$。该方法基于副控制分布和重正化。将原始非线性抛物线安德森模型方程分解为两个简单方程后，我们通过一些先验估计和平滑近似证明了全局适定性。此外，我们通过使用经典能量估计证明了解决方案的唯一性。