发表机构
University of Agder（阿格德尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建了高阶无界粗糙驱动项的框架，将其应用于含两类不同驱动项的粗糙输运方程，证明了该方程的适定性。
AI 中文摘要
我们构建了一个由向量场上的粗糙路径定义的高阶无界粗糙驱动项框架，这使我们能够为粗糙输运方程采用纯欧拉视角，其中驱动的粗糙路径向量场允许具有任意𝔭∈(1,∞)的时间𝔭-变差。我们利用该框架证明了含两个输运项方程的适定性：一项由上述具有时间𝔭-变差的粗糙路径向量场驱动，另一项由DiPerna–Lions型漂移向量场驱动。
英文摘要
We construct a framework for higher order unbounded rough drivers defined by rough paths over vector fields. This allows us to consider a purely Eulerian perspective for rough transport equations where the driving rough path vector field is allowed to have temporal $\mathfrak{p}$-variation for any $\mathfrak{p} \in (1,\infty)$. We use this framework to show the well-posedness of an equation with two transport terms; one driven by a rough path vector field with aforementioned $\mathfrak{p}$-variation in time, and the other driven by a DiPerna--Lions-type drift vector field.
