7 papers
Couette Taylor instabilities for counter-rotating cylinders in the small-gap regime
Dongfen Bian, Emmanuel Grenier, Gérard Iooss +1
We study the Couette Taylor instabilities for an incompressible viscous fluid between two coaxial cylinders of nearly equal radii, allowing counter-rotation with the ratio of rotat…
Subcritical bifurcations of shear flows
Dongfen Bian, Shouyi Dai, Emmanuel Grenier
It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity is small enough, provided the ho…
Stability and instability of small BGK waves
Dongfen Bian, Emmanuel Grenier, Wenrui Huang +1
The aim of this article is to prove that the linear stability or instability of small Bernstein-Green-Kruskal (BGK) waves is determined by the sign of the derivative of their energ…
Couette Taylor instabilities in the small-gap regime
Dongfen Bian, Emmanuel Grenier, Gérard Iooss +1
The Couette-Taylor instability occurs in a viscous fluid confined between two coaxial rotating cylinders. When the Taylor number surpasses a critical value, the stable Couette flow…
The dispersion relation of Tollmien-Schlichting waves
Dongfen Bian, Shouyi Dai, Emmanuel Grenier
It is well-known that shear flows in a strip or in the half plane are unstable for the Navier-Stokes equations if the viscosity is small enough, provided the horizontal wave n…
Bifurcations of viscous boundary layers in the half space
Dongfen Bian, Emmanuel Grenier, Gérard Iooss
It is well-established that shear flows are linearly unstable provided the viscosity is small enough, when the horizontal Fourier wave number lies in some interval, between the so-…