{
  "id": "2004.11264",
  "version": "v1",
  "published": "2020-04-23T15:47:34.000Z",
  "updated": "2020-04-23T15:47:34.000Z",
  "title": "Analytic regularity for the incompressible Navier-Stokes equations in polygons",
  "authors": [
    "Carlo Marcati",
    "Christoph Schwab"
  ],
  "categories": [
    "math.AP",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In a plane polygon $P$ with straight sides, we prove analytic regularity of the Leray-Hopf solution of the stationary, viscous, and incompressible Navier-Stokes equations. We assume small data, analytic volume force and no-slip boundary conditions. Analytic regularity is quantified in so-called countably normed, corner-weighted spaces with homogeneous norms. Implications of this analytic regularity include exponential smallness of Kolmogorov $N$-widths of solutions, exponential convergence rates of mixed $hp$-discontinuous Galerkin finite element and spectral element discretizations and of model order reduction techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-23T15:47:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76N10",
      "35A20"
    ],
    "keywords": [
      "incompressible navier-stokes equations",
      "analytic regularity",
      "model order reduction techniques",
      "assume small data",
      "exponential convergence rates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}