{
  "id": "2305.18142",
  "version": "v1",
  "published": "2023-05-29T15:12:54.000Z",
  "updated": "2023-05-29T15:12:54.000Z",
  "title": "A wavelet-inspired $L^3$-based convex integration framework for the Euler equations",
  "authors": [
    "Vikram Giri",
    "Hyunju Kwon",
    "Matthew Novack"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work, we develop a wavelet-inspired, $L^3$-based convex integration framework for constructing weak solutions to the three-dimensional incompressible Euler equations. The main innovations include a new multi-scale building block, which we call an intermittent Mikado bundle; a wavelet-inspired inductive set-up which includes assumptions on spatial and temporal support, in addition to $L^p$ and pointwise estimates for Eulerian and Lagrangian derivatives; and sharp decoupling lemmas, inverse divergence estimates, and space-frequency localization technology which is well-adapted to functions satisfying $L^p$ estimates for $p$ other than $1$, $2$, or $\\infty$. We develop these tools in the context of the Euler-Reynolds system, enabling us to give both a new proof of the intermittent Onsager theorem from [32] in this paper, and a proof of the $L^3$-based strong Onsager conjecture in the companion paper [22].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-29T15:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "35D30"
    ],
    "keywords": [
      "convex integration framework",
      "three-dimensional incompressible euler equations",
      "intermittent onsager theorem",
      "intermittent mikado bundle",
      "space-frequency localization technology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}