论文标题
无树规律结构的方法：准线性方程的常规情况
A tree-free approach to regularity structures: The regular case for quasi-linear equations
论文作者
论文摘要
我们对Otto，Sauer，Smith和Weber引入的规律性结构和模型进行了动力和温和的介绍，这些结构和模型属于Hairer的框架，但具有比树木给出的更贪婪的索引。我们在这里这样做以实现简单的准线性抛物线方程，并假设驾驶噪声是如此规则，以至于不需要重新归一化。我们介绍了抽象模型空间$ \ MATHSF {T} $及其分级，Pre-Model $ \Mathbfπ$，中心模型$π_x$，结构组$ \ Mathsf {G} $和重新中心转换$γ__{xy} $。使用集成和重建，我们在$π_x$和$γ_{xy} $上建立了所需的估计，这是确定性的，因为我们处理了常规情况。
We give a motivation and gentle introduction into the regularity structure and model introduced by Otto, Sauer, Smith and Weber, which fall into the framework of Hairer, but have a greedier index set than the one given by trees. We do this here for a simple quasi-linear parabolic equation and assume that the driving noise is so regular that no renormalization is needed. We introduce the abstract model space $\mathsf{T}$ and its grading, the pre-model $\mathbfΠ$, the centered model $Π_x$, the structure group $\mathsf{G}$, and the re-centering transformations $Γ_{xy}$. Using integration and reconstruction, we establish the desired estimates on $Π_x$ and $Γ_{xy}$, which here are deterministic since we deal with the regular case.
