Regularity and Expansion for Steady Prandtl Equations
Regularity and Expansion for Steady Prandtl Equations
复制标题
DOI：
10.1007/s00220-021-03964-9
复制
发表时间：
2019-03
影响因子：
2.4
通讯作者：
Yan Guo;Sameer Iyer
中科院分区：
文献类型：
--
作者：
Yan Guo;Sameer Iyer
由于边界附近的简并性，自 Oleinik 的著名工作以来，稳定普朗特方程解的高度正则性问题一直是一个长期悬而未决的问题。在没有外部压力的情况下，我们肯定地解决了这个悬而未决的问题。我们的方法基于商的能量估计，即通过线性导数 Prandtl (LDP) 方程的经典 Prandtl 解。因此，我们的正则性结果导致普朗特层展开到任意阶的构造。
Due to degeneracy near the boundary, the question of high regularity for solutions to the steady Prandtl equations has been a longstanding open question since the celebrated work of Oleinik. We settle this open question in affirmative in the absence of an external pressure. Our method is based on energy estimates for the quotient,,being the classical Prandtl solution, via the linear derivative Prandtl (LDP) equation. As a consequence, our regularity result leads to the construction of Prandtl layer expansion up to any order.