论文标题
具有非线性阻尼项的粗略微分方程的先验边界
A priori bounds for rough differential equations with a non-linear damping term
论文作者
论文摘要
We consider a rough differential equation with a non-linear damping drift term: \begin{align*} dY(t) = - |Y|^{m-1} Y(t) dt + σ(Y(t)) dX(t), \end{align*} where $X$ is a branched rough path of arbitrary regularity $α>0$, $m>1$ and where $σ$ is smooth and satisfies an $ m $和$α$依赖的增长物业。我们显示了一个强大的先验约束，其中包括$ y $ y $，即固定的$ t> 0 $在$ y（t）$上的限制均均匀地保留在所有初始datum $ y（0）$的选择上。证明方法是基于钱德拉，莫纳特和韦伯的最新作品的先验范围，该范围是$ ϕ^4 $ spde在任意的亚临界维度上的。一个关键的新成分是代数框架的扩展，该框架允许根据最低水平的规律性条件在相干控制的粗糙路径的高阶条件下得出估计值。
We consider a rough differential equation with a non-linear damping drift term: \begin{align*} dY(t) = - |Y|^{m-1} Y(t) dt + σ(Y(t)) dX(t), \end{align*} where $X$ is a branched rough path of arbitrary regularity $α>0$, $m>1$ and where $σ$ is smooth and satisfies an $m$ and $α$-dependent growth property. We show a strong a priori bound for $Y$, which includes the "coming down from infinity" property, i.e. the bound on $Y(t)$ for a fixed $t>0$ holds uniformly over all choices of initial datum $Y(0)$. The method of proof builds on recent work by Chandra, Moinat and Weber on a priori bounds for the $ϕ^4$ SPDE in arbitrary subcritical dimension. A key new ingredient is an extension of the algebraic framework which permits to derive an estimate on higher order conditions of a coherent controlled rough path in terms of the regularity condition at lowest level.
