Archive for Rational Mechanics and Analysis· 2026Q1
Structural Stability of Prandtl Boundary Layers in the Entire Subsonic Regime
- 1citations
- Q1SCImago
- 2026year
Short summary
The study establishes the structural stability of shear flow boundary layer profiles for 2D steady compressible Navier-Stokes equations across the entire subsonic regime, providing the first rigorous justification for the low Mach number limit with Prandtl-type boundary layers.
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Key points
- Establishes structural stability for shear flow boundary layers in 2D steady compressible Navier-Stokes equations.
- Stability estimates are uniform across the entire subsonic regime.
- Provides the first rigorous justification for the low Mach number limit with Prandtl-type boundary layers.
- Proof utilizes quasi-compressible-Stokes iteration and frequency-dependent analysis of density-velocity coupling.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Archive for Rational Mechanics and Analysis, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics