Affordable Access

Publisher Website

Well-posedness and scattering for the KP-II equation in a critical space

Authors
Journal
Annales de l Institut Henri Poincare (C) Non Linear Analysis
0294-1449
Publisher
Elsevier
Publication Date
Volume
26
Issue
3
Identifiers
DOI: 10.1016/j.anihpc.2008.04.002
Keywords
  • Kadomtsev–Petviashvili-Ii Equation
  • Scale Invariant Space
  • Well-Posedness
  • Scattering
  • Bilinear Estimates
  • Boundedp-Variation

Abstract

Abstract The Cauchy problem for the Kadomtsev–Petviashvili-II equation ( u t + u x x x + u u x ) x + u y y = 0 is considered. A small data global well-posedness and scattering result in the scale invariant, non-isotropic, homogeneous Sobolev space H ˙ − 1 2 , 0 ( R 2 ) is derived. Additionally, it is proved that for arbitrarily large initial data the Cauchy problem is locally well-posed in the homogeneous space H ˙ − 1 2 , 0 ( R 2 ) and in the inhomogeneous space H − 1 2 , 0 ( R 2 ) , respectively.

There are no comments yet on this publication. Be the first to share your thoughts.