{
  "id": "2001.09204",
  "version": "v1",
  "published": "2020-01-24T21:39:24.000Z",
  "updated": "2020-01-24T21:39:24.000Z",
  "title": "Propagation of $L^p_β$-norm, $ 1<p\\le \\infty$, for the system of Boltzmann equations for monatomic gas mixtures",
  "authors": [
    "Erica de la Canal",
    "Irene M. Gamba",
    "Milana Pavić-Čolić"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "With the existence and uniqueness of a vector value solution for the full non-linear homogeneous Boltzmann system of equations describing multi-component monatomic gas mixtures for binary interactions proved [8], we present in this manuscript several properties for such a solution. We start by proving the gain of integrability of the gain term of the multispecies collision operator, extending the work done previously for the single species case [3]. In addition, we study the integrability properties of the multispecies collision operator as a bilinear form, revisiting and expanding the work done for a single gas [2]. With these estimates, together with a control by below for the loss term of the collision operator as in [8], we develop the propagation for the polynomially and exponentially $\\beta$-weighted $L^p_\\beta$-norms for the vector value solution. Finally, we extend such $L^p_\\beta$-norms propagation property to $p=\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-24T21:39:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boltzmann equations",
      "vector value solution",
      "propagation",
      "multispecies collision operator",
      "full non-linear homogeneous boltzmann system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}