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arXiv · 2609.25702

Asymptotic Stability of Steady Prandtl Equations with Suction

Yonghao Li·Yong Wang
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Abstract

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.

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Yonghao Li, Yong Wang. 2026-09-22. Asymptotic Stability of Steady Prandtl Equations with Suction. https://arxiv.org/abs/2609.25702

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