{
  "id": "1805.08987",
  "version": "v1",
  "published": "2018-05-23T07:36:51.000Z",
  "updated": "2018-05-23T07:36:51.000Z",
  "title": "Local bifurcation of steady almost periodic water waves with constant vorticity",
  "authors": [
    "Wei Luo",
    "Zhaoyang Yin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we mainly investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using conformal mappings, one can change the free boundary problem into a fixed boundary problem with some unknown functions in the boundary condition. By virtue of the Hilbert transform, the problem is equivalent to a quasilinear pseudodifferential equation for a almost periodic function of one variable. The bifurcation theory ensures us to obtain a existence result. Our existence result generalizes and covers the recent result in \\cite{Constantin2011v}. Moreover, our result implies a non-uniqueness result at the same bifurcation point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-23T07:36:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic water waves",
      "constant vorticity",
      "local bifurcation",
      "free surface",
      "dimensional euler equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}