{
  "id": "2211.16215",
  "version": "v1",
  "published": "2022-11-29T13:49:32.000Z",
  "updated": "2022-11-29T13:49:32.000Z",
  "title": "From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations",
  "authors": [
    "Tobias Barker",
    "Christophe Prange"
  ],
  "comment": "In honor of Carlos Kenig's 70th birthday; 4 figures, 3 tables",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this short survey paper, we focus on some new developments in the study of the regularity or potential singularity formation for solutions of the 3D Navier-Stokes equations. Some of the motivating questions are: Are certain norms accumulating/concentrating on small scales near potential blow-up times? At what speed do certain scale-invariant norms blow-up? Can one prove explicit quantitative regularity estimates? Can one break the criticality barrier, even slightly? We emphasize that these questions are closely linked together. Many recent advances for the Navier-Stokes equations are directly inspired by results and methods from the field of nonlinear dispersive equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-29T13:49:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A99",
      "35B44",
      "35B65",
      "35Q30",
      "76D05"
    ],
    "keywords": [
      "developments",
      "concentration",
      "short survey paper",
      "explicit quantitative regularity estimates",
      "scale-invariant norms blow-up"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}