{
  "id": "2301.06258",
  "version": "v1",
  "published": "2023-01-16T04:50:06.000Z",
  "updated": "2023-01-16T04:50:06.000Z",
  "title": "Attractors for the Navier-Stokes-Cahn-Hilliard System with Chemotaxis and Singular Potential in 2D",
  "authors": [
    "Jingning He"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2104.01010",
  "categories": [
    "math.AP"
  ],
  "abstract": "We analyze the long-time behavior of solutions to a Navier-Stokes-Cahn--Hilliard-Oono system with chemotaxis effects and physically relevant singular potential. This model also includes some significant mechanisms such as active transport and chemotaxis effects. The system couples the Navier-Stokes equations for the fluid velocity, a convective Cahn-Hilliard equation for the phase-field variable and a diffusion equation for the nutrient density. For the initial boundary value problem in a smooth bounded domain $\\Omega\\subset \\mathbb{R}^2$, we prove the the existence of the global attractor in a suitable phase space. Furthermore, we obtain the existence of an exponential attractor, and it can be implied that the global attractor is of finite fractal dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-16T04:50:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35A02",
      "35K35",
      "35Q92",
      "76D05"
    ],
    "keywords": [
      "navier-stokes-cahn-hilliard system",
      "global attractor",
      "initial boundary value problem",
      "chemotaxis effects",
      "finite fractal dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}