Work

Structural Stability of Prandtl Boundary Layers in the Entire Subsonic Regime

Year: 2026

Type: article

Abstract: Despite the physical significance of the compressible Navier–Stokes equations in the presence of strong boundary layers, rigorous mathematical theories in this area remain at an early stage of development. In this paper, we establish the structural stability of shear flow boundary layer profiles for the two-dimensional steady compressible Navier–Stokes equations. The stability estimates are uniform across the entire subsonic regime. As a byproduct, we provide the first rigorous justification of the low Mach number limit in the presence of Prandtl-type boundary layers. The proof relies on the quasi-compressible-Stokes iteration introduced in [41], combining a frequency-dependent analysis of the density-velocity coupling, and the identification of structural cancellations in higher-order estimates.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-026-02241-0

Authors: Shengxin Li, Tong Yang, Zhu Zhang

Institution: Hong Kong Polytechnic University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: University Grants Committee, Hong Kong Polytechnic University