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Spectral stability of Prandtl boundary layers: An overview
-
Emmanuel Grenier
,
Yan Guo
Published/Copyright:
October 7, 2015
Abstract
In this paper we show how the stability of Prandtl boundary layers is linked to the stability of shear flows in the incompressible Navier–Stokes equations. We then recall classical physical instability results, and give a short educational presentation of the construction of unstable modes for Orr–Sommerfeld equations. We end the paper with a conjecture concerning the validity of Prandtl boundary layer asymptotic expansions.
Received: 2015-1-6
Revised: 2015-7-2
Accepted: 2015-8-14
Published Online: 2015-10-7
Published in Print: 2015-11-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Time delay and Lagrangian approximation for Navier–Stokes flow
- Compressible Navier–Stokes limit of binary mixture of gas particles
- On asymptotic stability of global solutions in the weak L2 space for the two-dimensional Navier–Stokes equations
- A regularity criterion of Serrin-type for the Navier–Stokes equations involving the gradient of one velocity component
- Steady-state flow of a shear-thinning liquid in an unbounded pipeline system
- Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions
- On the steady flow of reactive gaseous mixture
- Spectral stability of Prandtl boundary layers: An overview
Articles in the same Issue
- Frontmatter
- Time delay and Lagrangian approximation for Navier–Stokes flow
- Compressible Navier–Stokes limit of binary mixture of gas particles
- On asymptotic stability of global solutions in the weak L2 space for the two-dimensional Navier–Stokes equations
- A regularity criterion of Serrin-type for the Navier–Stokes equations involving the gradient of one velocity component
- Steady-state flow of a shear-thinning liquid in an unbounded pipeline system
- Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions
- On the steady flow of reactive gaseous mixture
- Spectral stability of Prandtl boundary layers: An overview
