{
  "id": "1806.04006",
  "version": "v1",
  "published": "2018-06-11T14:14:10.000Z",
  "updated": "2018-06-11T14:14:10.000Z",
  "title": "An $L^{p}$--approach to the well-posedness of transport equations associated to a regular field",
  "authors": [
    "Luisa Arlotti",
    "Bertrand Lods"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate transport equations associated to a Lipschitz field on some subspace of $\\mathbb{R}^N$ endowedwith a general measure $\\mu$ in $L^{p}$-spaces $1 < p <\\infty$, extending the results obtained in two previous contributions of the author in the $L^{1}$-context. We notably prove the well-posedness of boundary-value transport problems with a large variety of boundary conditions. New explicit formula for the transport semigroup are in particular given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-11T14:14:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transport equations",
      "regular field",
      "well-posedness",
      "boundary-value transport problems",
      "lipschitz field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}