{
  "id": "2012.11875",
  "version": "v1",
  "published": "2020-12-22T08:26:02.000Z",
  "updated": "2020-12-22T08:26:02.000Z",
  "title": "Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field",
  "authors": [
    "Dongfen Bian",
    "Shouyi Dai",
    "Jingjing Mao"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "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 $(\\mathbf{u}_{sh} = (y,0), \\mathbf{b}_{sh} = (1,0), p_{sh} = 0, \\theta_{sh} = 0$). 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 $\\partial_{xy}(-\\Delta)^{-1}j$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-22T08:26:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "2d boussinesq system",
      "uniform magnetic field",
      "couette flow",
      "nonlinear stability",
      "fourier multiplier operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}