Boundary layers and inviscid limits

Appears in collection : 2026 - T2 - WS2 - Instabilities and transitions in geophysical flows

I will discuss several recent results on vanishing-viscosity limits for incompressible Navier-Stokes flows near boundaries. I will begin with boundary vorticity estimates and their application to weak inviscid limits near plug flow in a periodic tunnel, giving short-time control of deviations from the shear profile. I will then present unconditional $L^2$ bounds on boundary layer separation between Leray-Hopf Navier-Stokes solutions and smooth Euler flows in bounded domains. Finally, I will discuss joint work on non-characteristic boundaries, where one can quantify energy dissipation and enstrophy production near outflow in terms of the boundary mismatch between Navier-Stokes and Euler flows.

Co-author: Alexis Vasseur

Information about the video

Date of recording 19/05/2026
Date of publication 06/06/2026
Institution IHP
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Service audiovisuel de l'IHP
Format MP4
Venue IHP - Hermite Amphitheater

Domain(s)

Analysis of PDEs

Bibliography

Alexis F. Vasseur, Jincheng Yang: Boundary vorticity estimates for Navier–Stokes and application to the inviscid limit, SIAM Journal on Mathematical Analysis, 55: 3081–3107. (2023)
Alexis F. Vasseur, Jincheng Yang: Layer separation of the 3D incompressible Navier–Stokes equation in a bounded domain, Communications in Partial Differential Equations, 49: 381–409. (2024)
Jincheng Yang, Vincent R. Martinez, Anna L. Mazzucato, Alexis F. Vasseur: Energy dissipation near the outflow boundary in the vanishing viscosity limit, Indiana University Mathematics Journal, forthcoming. (2025)