Instability of shear flows with neutral embedded eigenvalues
Abstract
We study the linear stability of a class of monotone shear flows. When the associated Rayleigh operator possesses a neutral embedded eigenvalue, we show that solutions of the linearized system may exhibit arbitrarily large growth in both the $L^\infty$ and $L^2$ norms. Moreover, when the embedded eigenvalue is multiple, we prove that the instability becomes stronger and explicitly construct solutions that grow linearly in time. This instability originates from the non-normality of the Rayleigh operator.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Advanced Mathematical Physics Problems
Navier-Stokes equation solutions
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 February 2026
- Language
- EN
- Document type
- Preprint