Description

Book Synopsis
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable $x$) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension.

Table of Contents
  • Introduction and main result
  • Functional setting
  • Transversality properties of degenerate KAM theory
  • Nash-Moser theorem and measure estimates
  • Approximate inverse
  • The linearized operator in the normal directions
  • Almost diagonalization and invertibility of $\mathcal{L}_{\omega}$
  • The Nash-Moser iteration
  • Appendix A. Tame estimates for the flow of pseudo-PDEs
  • Bibliography.

Quasiperiodic Standing Wave Solutions of

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    A Paperback by Massimiliano Berti, Riccardo Montalto

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 4/30/2020 12:00:00 AM
      ISBN13: 9781470440695, 978-1470440695
      ISBN10: 1470440695

      Description

      Book Synopsis
      The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable $x$) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension.

      Table of Contents
      • Introduction and main result
      • Functional setting
      • Transversality properties of degenerate KAM theory
      • Nash-Moser theorem and measure estimates
      • Approximate inverse
      • The linearized operator in the normal directions
      • Almost diagonalization and invertibility of $\mathcal{L}_{\omega}$
      • The Nash-Moser iteration
      • Appendix A. Tame estimates for the flow of pseudo-PDEs
      • Bibliography.

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