rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle
  name:
    name part: Berti, Massimiliano.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Delort, Jean-Marc.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 269 p. 3 illus. online resource.
  abstract: The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
  note: by Massimiliano Berti, Jean-Marc Delort.
  subject:
    topic: Partial differential equations
  subject:
    topic: Fourier analysis
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Functional analysis
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Fourier Analysis
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Functional Analysis
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes of the Unione Matematica Italiana, 24
  identifier: 9783319994864
  identifier: https://doi.org/10.1007/978-3-319-99486-4
  record info:
    record creation date: 181102
    record change date: 20191025161152.0
    record identifier: 978-3-319-99486-4