A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions
Analysis of PDEs
2026-01-01 v1
Abstract
In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the linearized equations is shown via the operator method of Lafitte and Nguyen (2022). Hence, we prove the nonlinear instability by adapting the framework of Desjardins and Grenier (2003) studying some classes of viscous boundary layers to obtain two separated solutions at escaping time. Our work performs a different approach from that of Ding, Li and Xin (2018).
Keywords
Cite
@article{arxiv.2512.23946,
title = {A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions},
author = {Tien-Tai Nguyen},
journal= {arXiv preprint arXiv:2512.23946},
year = {2026}
}