发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院数学与系统科学研究院; 中国科学院大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了壁面吸气下稳态Prandtl方程的全局渐近稳定性，通过von Mises变换和Hardy型估计，实现了任意代数衰减率的下游衰减。
AI 中文摘要
尽管具有物理重要性，但在严格的偏微分方程分析中，壁面吸气下Prandtl边界层的稳定性仍相对未被探索。本文中，我们建立了吸气廓线的全局（关于$x$）渐近稳定性。对于任意给定的$x$中的代数衰减率，我们证明，具有足够快空间衰减的足够小的入流扰动会产生该速率的下游衰减。von Mises变换将Prandtl系统简化为一个具有有利方向对流项的退化抛物方程。我们首先在相关的均匀抛物问题中识别下游衰减机制，然后使用一个尖锐的Hardy型估计来控制边界退化。综合这些论证，我们得到了原始Prandtl系统的稳定性和衰减。
英文摘要
Despite its physical importance, the stability of Prandtl boundary layers under wall suction remains relatively unexplored in rigorous PDE analysis. In this paper, we establish the global-in-$x$ asymptotic stability of a suction profile. For any prescribed algebraic decay rate in $x$, we prove that sufficiently small inflow perturbations with sufficiently rapid spatial decay yield downstream decay at that rate. The von Mises transformation reduces the Prandtl system to a degenerate parabolic equation with a favorably directed convection term. We first identify the downstream decay mechanism in an associated uniformly parabolic problem, then control the boundary degeneracy using a sharp Hardy-type estimate. Together, these arguments yield stability and decay for the original Prandtl system.
Comments29 pages
