On the Cauchy-problem for Generalized Kadomtsev-petviashvili-ii Equations

  title={On the Cauchy-problem for Generalized Kadomtsev-petviashvili-ii Equations},
  author={Axel Gr¨unrock}
  • Axel Gr¨unrock
The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation ut + uxxx + ∂ −1 x uyy = (u l)x, l ≥ 3, is shown to be locally well-posed in almost critical anisotropic Sobolev spaces. The proof combines local smoothing and maximal function estimates as well as bilinear refinements of Strichartz type inequalities via multilinear interpolation in X s,b-spaces. 
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On the local well-posedness of the Kadomtsev-Petviashvili II equation

  • M Hadac
  • Thesis
  • 2007

Local well posedness for modified Kadomstev-Petviashvili equations

  • C E Kenig, S N Ziesler
  • Differential Integral Equations
  • 2005

Maximal function estimates with applications to a modified Kadomstev-Petviashvili equation Commun

  • C E Kenig, S N Ziesler
  • Pure Appl. Anal
  • 2005

Local and global Cauchy problems for the Kadomtsev-Petviashvili (KPII) equation in Sobolev spaces of negative indices

  • P Isaza, J Mejia
  • Comm. Partial Differential Equations
  • 2001

On the local regularity of the Kadomtsev-Petviashvili-II equation

  • H Takaoka, N Tzvetkov
  • IMRN
  • 2001

Global low regularity solutions for Kadomtsev-Petviashvili equation, Differential Integral Equations

  • N Tzvetkov
  • Global low regularity solutions for Kadomtsev…
  • 2000

Asymptotocs for large time of global solutions to the generalized Kadomtsev-Petviashvili equation

  • N Hayashi, P I Naumkin, J.-C Saut
  • Commun. Math. Phys
  • 1999

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