{
  "id": "2304.08985",
  "version": "v1",
  "published": "2023-04-18T13:33:16.000Z",
  "updated": "2023-04-18T13:33:16.000Z",
  "title": "Weak and classical solutions to an asymptotic model for atmospheric flows",
  "authors": [
    "Bogdan-Vasile Matioc",
    "Luigi Roberti"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the model as a quasilinear parabolic evolution problem in an appropriate functional analytic framework and by using abstract theory for such problems. Moreover, for $L_2$-initial data, we construct global weak solutions by employing a two-step approximation strategy based on a Galerkin scheme, where an equivalent formulation of the problem in terms of a new variable is used. Compared to the original model, the latter has the advantage that the $L_2$-norm is a Liapunov functional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-18T13:33:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D30",
      "35K59",
      "35Q86"
    ],
    "keywords": [
      "classical solutions",
      "atmospheric flows",
      "asymptotic model",
      "construct global weak solutions",
      "quasilinear parabolic evolution problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}