arXiv subjects

Shouyi Dai

Publications and source records attributed to Shouyi Dai.

3 recordsLinked to original sources

arXiv2026

Subcritical bifurcations of shear flows

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 $ν$ is small enough, provided the horizontal wave number $α$ lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical.

math.AP↗

arXiv2025

The dispersion relation of Tollmien-Schlichting waves

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 $ν$ is small enough, provided the horizontal wave number $α$ lies in a small interval, between the so called lower and upper marginal stability curves. The corresponding instabilities are called Tollmien-Schlichting waves. In this letter, we give a simple presentation of the dispersion relation of these waves and study its mathematical properties.

math.AP↗

arXiv2020

Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field

In this paper, we consider the Boussinesq equations with magnetohydrodynamics convection in the domain $\mathbb{T} \times \mathbb{R}$ and establishes the nonlinear stability of the Couette flow $(\mathbf{u}_{sh} = (y,0), \mathbf{b}_{sh} = (1,0), p_{sh} = 0, θ_{sh} = 0$). The novelty in this paper is that we design a new Fourier multiplier operator by using the properties of the enhanced dissipation to overcome the difficult term $\partial_{xy}(-Δ)^{-1}j$ in the linearized and nonlinear system. Then, we prove the asymptotic stability for the linearized system. Finally, we establish the nonlinear stability for the full system by bootstrap principle.

math.AP↗