{
  "id": "2104.09870",
  "version": "v1",
  "published": "2021-04-20T10:03:48.000Z",
  "updated": "2021-04-20T10:03:48.000Z",
  "title": "Asymptotic behaviors for Blackstock's model of thermoviscous flow",
  "authors": [
    "Wenhui Chen",
    "Ryo Ikehata",
    "Alessandro Palmieri"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a fundamental model in nonlinear acoustics, precisely, the general Blackstock's model (that is, without Becker's assumption) in the whole space $\\mathbb{R}^n$. This model describes nonlinear acoustics in perfect gases under the irrotational flow. By means of the Fourier analysis we will derive $L^2$ estimates for the solution of the linear homogeneous problem and its derivatives. Then, we will apply these estimates to study three different topics: the optimality of the decay estimates in the case $n\\geqslant 5$ and the optimal growth rate for the $L^2$-norm of the solution for $n=3,4$; the singular limit problem in determining the first- and second-order profiles for the solution of the linear Blackstock's model with respect to the small thermal diffusivity; the proof of the existence of global (in time) small data Sobolev solutions with suitable regularity for a nonlinear Blackstock's model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-20T10:03:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic behaviors",
      "thermoviscous flow",
      "small data sobolev solutions",
      "nonlinear acoustics",
      "small thermal diffusivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}