Related papers: On Enhanced Dissipation for the Boussinesq Equatio…
This short note provides explicit solutions to the linearized Boussinesq equations around the stably stratified Couette flow posed on $\mathbb{T}\times\mathbb{R}$. We consider the long-time behavior of such solutions and prove inviscid…
In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow $(1-y^2,0)$ in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized…
In this paper we study the zero-viscosity limit of $2$-D Boussinesq equations with vertical viscosity and zero diffusivity, which is a nonlinear system with partial dissipation arising in atmospheric sciences and oceanic circulation. The…
In this paper, we prove the stability threshold of $\alpha\leq \frac13$ for 2D Boussinesq equations around the Couette flow in $\mathbb{T}\times \mathbb{R}$ with Richardson number $\gamma^2>\frac14$ and different viscosity $\nu$ and thermal…
This paper investigates the large-time behavior of a buoyancy-driven fluid without thermal diffusion under Navier-slip boundary conditions in a bounded domain with Lipschitz-continuous second derivatives. After establishing improved…
We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted…
This paper addresses the stability and large-time behavior problem on the perturbations near the hydrostatic balance of the two dimensional Boussinesq system, taking into account vertical dissipation and horizontal thermal diffusion. The…
In this paper, we investigate the quantitative stability for the 2D Couette flow on the infinite channel $\mathbb{R}\times [-1,1]$ with non-slip boundary condition. Compared to the case $\mathbb{T}\times [-1,1]$, we establish the stability…
In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We investigate the stability of the 2-D Navier-Stokes equations in the infinite channel $\mathbb{R}\times [-1,1]$ with the Navier-slip boundary condition. We show that if the initial perturbations $\omega^{in}$ around the Couette flow…
The aim of this communication is to present a simplified, yet rigorous, deduction of the Boussinesq approximated governing equations for buoyant flows. In order to carry out the core deduction procedure, a simplified version of the manifold…
The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…
This paper is concerned with the asymptotic stability of certain stationary solution to Boussinesq equations without thermal conduction in the infinite flat strip $\Omega=\mathbb{R}\times (0,1)$. It is shown that the solution starting from…
In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain $\mathbb{T}\times \mathbb{R}$. In the inviscid case there is a generic…
In this paper, we investigate linear stability properties of the 2D isentropic compressible Euler equations linearized around a shear flow given by a monotone profile, close to the Couette flow, with constant density, in the domain…
We consider the 2D Boussinesq equations with viscous but without thermal dissipation and observe that in any neighborhood of Couette flow and hydrostatic balance (with respect to local norms) there are time-dependent traveling wave…
In this work, a novel Boussinesq system is put forward. The system is naturally nonlinearly entropy/energy-stable, and is designed for problems with sharply varying bathymetric features. The system is flexible and allows tuning of the…
The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the $L^2$-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq…
This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal…