Related papers: On Enhanced Dissipation for the Boussinesq Equatio…
We study the linear asymptotic stability of stably stratified monotone shear flows for the Boussinesq equations in the periodic channel. By means of the limiting absorption principle, we obtain a precise description of the inviscid damping…
In this paper, we study the asymptotic stability for the two-dimensional Navier-Stokes Boussinesq system around the Couette flow with small viscosity $\nu$ and small thermal diffusion $\mu$ in a finite channel. In particular, we prove that…
We study the Sobolev stability thresholds of 2d dissipative fluid equations around Couette flow on the domain $\mathbb T\times \mathbb R$. We prove a bound for general nonlinear interactions, which, for several fluid equations, reduces the…
The system of the Boussinesq equations is one of the most important models for geophysical fluids. This paper focuses on the initial-boundary problem of the 3D incompressible anisotropic Boussinesq system with horizontal dissipation. The…
We study the two dimensional viscous Boussinesq equations, which model stratified flows in a circular domain under the influence of a general gravitational potential $f$. First, we show that the Boussinesq equations admit steady-state…
In this paper, we study the nonlinear stability of a steady circular flow created between two rotating concentric cylinders. The dynamics of the viscous fluid are described by 2D Navier-Stokes equations. We adopt scaling variables. For the…
In this paper, we consider the stability threshold for the shear flows of the Boussinesq system in a domain $\mathbb{T} \times \mathbb{R}$. The main goal is to prove the nonlinear stability of the shear flow $(U^S,\Theta^S)=((e^{\nu…
The stability problem for the 2D Navier-Stokes equations with dissipation in only one direction on $\mathbb R^2$ is not fully understood. This dissipation is in the intermediate regime between the fully dissipative Navier-Stokes and the…
In this article we consider the 2D Navier-Stokes equations with variable viscosity depending on the vertical position. As our main result we establish linear enhanced dissipation near the non-affine stationary states replacing Couette flow.…
In this paper, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier-Stokes system around the symmetric flow in a finite channel with the non-slip boundary condition. As an immediate consequence, we…
In this paper, we investigate the long-time behavior of the two-dimensional incompressible Boussinesq system with kinematic viscosity in a periodic channel, focusing on instability and asymptotic stability near hydrostatic equilibria.…
We consider the solution to the 2D Navier-Stokes equations around the Poiseuille flow $(y^2,0)$ on $\mathbb{T}\times\mathbb{R}$ with small viscosity $\nu>0$. Via a hypocoercivity argument, we prove that the $x-$dependent modes of the…
In this expository note we discuss our recent work [arXiv:1306.5028] on the nonlinear asymptotic stability of shear flows in the 2D Euler equations of ideal, incompressible flow. In that work it is proved that perturbations to the Couette…
Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$. We prove the enhanced dissipation phenomenon for the linearized isentropic compressible…
In this manuscript, we consider the $3$D Boussinesq equations for stably stratified fluids with the horizontal viscosity and thermal diffusivity and investigate the large time behavior of the solutions. Making use of the anisotropic…
In this paper, we prove the stability of Couette flow for 2D Navier-Stokes Boussinesq system without thermal diffusivity for the initial perturbation in Gevrey-$\frac{1}{s}$, ($1/3<s\leq 1$). The synergism of density mixing, vorticity…
In this paper, we develop a stability threshold theorem for the 2D incompressible Navier-Stokes equations on the channel, supplemented with the no-slip boundary condition. The initial datum is close to the Couette flow in the following…
We are concerned with the linear stability of the Couette flow for the non-isentropic compressible Navier-Stokes equations with vanished shear viscosity in a domain $\mathbb{T}\times \mathbb{R}$. For a general initial data settled in…
This paper establishes the asymptotic stability threshold for the Couette flow $(y,0)$ under the 2D Boussinesq system in $\mathbb{R}^2$. It was proved that for initial perturbations in Sobolev spaces with controlled low horizontal…
Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…