3 papers
math.AP2026
Spectral analysis of the classical Rayleigh-Taylor instability with an upper free surface
Blake Barker, Tien-Tai Nguyen, Benjamin Settle
In this note, we are interested in the linear Rayleigh-Taylor instability problem for the incompressible fluid with an upper free surface. Using the spectral theory of self-adjoint…
math.AP2025
A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions
Tien-Tai Nguyen
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…
math.AP2023
Influence of capillary number on nonlinear Rayleigh-Taylor instability to the Navier-Stokes-Korteweg equations
Tien-Tai Nguyen
Motivated by Bresch, Desjardins, Gisclon and Sart (2008), in this paper, we study the influence of capillary number on an instability result related to the Navier-Stokes-Korteweg e…