论文标题
在均匀磁场中2D Boussinesq系统的COUETTE流量的稳定性
Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field
论文作者
论文摘要
在本文中，我们考虑域中具有磁性水力动力学对流的BousSinesQ方程，$ \ Mathbb {t} \ times \ Mathbb {r} $，并确定了Couette Flow flow $的非线性稳定性（1,0），p_ {sh} = 0，θ_{sh} = 0 $）。本文中的新颖性是，我们使用增强耗散的属性来克服困难的术语$ \ partial_ {xy}（ - δ）^{ - 1} J $在线性化和非线性系统中，我们设计了一个新的傅立叶乘数运算符。然后，我们证明了线性化系统的渐近稳定性。最后，我们通过引导原理建立了完整系统的非线性稳定性。
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.
