2025/08/18 by Ming Dong, Dong, Ming, Chao Wang +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2508.12965
openalex publication_date 2025/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper establishes the existence and uniqueness of classical solutions to the steady Triple-Deck equations, which describe incompressible boundary layer flow over localized roughness at high Reynolds numbers. The triple-deck theory was developed to overcome the Goldstein singularity in classical Prandtl boundary layer theory, capturing the interaction between the viscous sublayer, main layer, and upper layer when surface roughness of height O(\rm Re-\frac58) is present. The key ingredients of this paper include: (1) A decomposition separating roughness effects from nonlinear difficulties; (2) A novel Green's function using Airy functions that overcomes low-frequency singularities via the non-vanishing property of √(3)Ai(z)+Bi(z); (3) The introduction of weighted Sobolev norms \norm|\px|(1)/(18)y\frac16ωL2 of the vorticity yielding M-independent estimates for displacement A. As a byproduct, local uniqueness of Couette flow is established when F=0.