Tollmien–Schlichting waves in the subsonic regime

Nader Masmoudi, Yuxi Wang, Di Wu, Zhifei Zhang

Research output: Contribution to journalArticlepeer-review


The Tollmien–Schlichting (T-S) waves play a key role in the early stages of boundary layer transition. In a breakthrough work, Grenier, Guo, and Nguyen gave the first rigorous construction of the T-S waves of temporal mode for the incompressible fluid. Yang and Zhang recently made an important contribution by constructing the compressible T-S waves of temporal mode for certain boundary layer profiles with Mach number (Formula presented.). In this paper, we construct the T-S waves of both temporal mode and spatial mode to the linearized compressible Navier–Stokes system around the boundary layer flow in the whole subsonic regime (Formula presented.), including the Blasius profile. Our approach is based on a novel iteration scheme between the quasi-incompressible and quasi-compressible systems, with a key ingredient being the solution of an Orr–Sommerfeld-type equation using a new Airy–Airy–Rayleigh iteration instead of Rayleigh–Airy iteration introduced by Grenier, Guo, and Nguyen. We believe that the method developed in this work can be applied in solving other related problems for subsonic flows.

Original languageEnglish (US)
Article numbere12588
JournalProceedings of the London Mathematical Society
Issue number3
StatePublished - Mar 2024

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Tollmien–Schlichting waves in the subsonic regime'. Together they form a unique fingerprint.

Cite this