{
  "id": "2105.11287",
  "version": "v1",
  "published": "2021-05-24T14:18:10.000Z",
  "updated": "2021-05-24T14:18:10.000Z",
  "title": "Global existence for the Jordan--Moore--Gibson--Thompson equation in Besov spaces",
  "authors": [
    "Belkacem Said-Houari"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the Cauchy problem of a model in nonlinear acoustic, named the Jordan--Moore--Gibson--Thompson equation. This equation arises as an alternative model to the well-known Kuznetsov equation in acoustics. We prove global existence and optimal time decay of solutions in Besov spaces with a minimal regularity assumption on the initial data, lowering the regularity assumption required in \\cite{Racke_Said_2019} for the proof of the global existence. Using a time-weighted energy method with the help of appropriate Lyapunov-type estimates, we also extend the decay rate in \\cite{Racke_Said_2019} and show an optimal decay rate of the solution for initial data in the Besov space $\\dot{{B}}_{2,\\infty}^{-3/2}(\\mathbb{R}^3)$, which is larger than the Lebesgue space $L^1(\\R^3)$ due to the embedding $L^1(\\mathbb{R}% ^3)\\hookrightarrow \\dot{{B}}_{2,\\infty}^{-3/2}(\\mathbb{R}^3)$. Hence we removed the $L^1$-assumption on the initial data required in \\cite{Racke_Said_2019} in order to prove the decay estimates of the solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-24T14:18:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "besov space",
      "global existence",
      "jordan-moore-gibson-thompson equation",
      "initial data",
      "optimal time decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}