论文标题
（S）PDE的代数变形
Algebraic deformation for (S)PDEs
论文作者
论文摘要
我们基于前LIE产品的变形引入了一个新的代数框架。这使我们能够在ARXIV：1610.08468和ARXIV：2005.01649中使用规律性结构中的代数对象的新结构，用于在低规律性下得出分散PDES的一般方案。该结构还解释了Arxiv中的代数结构：1610.08468如何看作是屠夫 - 康涅斯肯尼尔群岛和提取 - 诱使Hopf代数的变形。我们首先通过Taylor变形将各种前LIE产品变形，然后应用Guin-Oudom程序，该程序为我们提供了一种关联产品，可以将其与已知的共同体进行比较。这项工作表明，在（S）PDES研究中，前LIE产品及其变形可能是一个核心对象。
We introduce a new algebraic framework based on the deformation of pre-Lie products. This allows us to provide a new construction of the algebraic objects at play in Regularity Structures in the work arXiv:1610.08468 and in arXiv:2005.01649 for deriving a general scheme for dispersive PDEs at low regularity. This construction also explains how the algebraic structure in arXiv:1610.08468 can be viewed as a deformation of the Butcher-Connes-Kreimer and the extraction-contraction Hopf algebras. We start by deforming various pre-Lie products via a Taylor deformation and then we apply the Guin-Oudom procedure which gives us an associative product whose adjoint can be compared with known coproducts. This work reveals that pre-Lie products and their deformation can be a central object in the study of (S)PDEs.
