Title: A simple construction of the dynamical $Φ^4_3$ model Show Chinese title

Title: 一个动态$Φ^4_3$模型的简单构造

Abstract: The $\Phi^4_3$ equation is a singular stochastic PDE with important applications in mathematical physics. Its solution usually requires advanced mathematical theories like regularity structures or paracontrolled distributions, and even local well-posedness is highly nontrivial. Here we propose a multiplicative transformation to reduce the periodic $\Phi^4_3$ equation to a well-posed random PDE. This leads to a simple and elementary proof of global well-posedness, which only relies on Schauder estimates, the maximum principle, and basic estimates for paraproducts, and in particular does not need regularity structures or paracontrolled distributions. Show Chinese abstract

Abstract: $\Phi^4_3$方程是一个具有重要应用的奇异随机偏微分方程。 其解通常需要高级数学理论，如正则性结构或准控制分布，甚至局部适定性也是高度非平凡的。 这里我们提出一种乘法变换，将周期性的$\Phi^4_3$方程转化为一个适定的随机偏微分方程。 这导致了一个简单且基本的全局适定性的证明，该证明仅依赖于Schauder估计、最大原理和对流产品的基本估计，并且特别不需要正则性结构或准控制分布。