### Well-posedness for the Kadomtsev-Petviashvili II equation

Hideo Takaoka

#### Abstract

We study the well-posedness for the Cauchy problem of the KP II equation. We prove the local well-posedness in the anisotropic Sobolev spaces $H_{x,y}^{-1/4+\epsilon,0}$ and in the anisotropic homogeneous Sobolev spaces $H_{x,y}^{-1/2+4\epsilon,0}\cap\dot{H}_{x,y}^{-1/2+\epsilon,0}$. The first result is an improvement of the result in $L^2$ obtained by J. Bourgain [2].

#### Article information

Source
Adv. Differential Equations Volume 5, Number 10-12 (2000), 1421-1443.

Dates
First available in Project Euclid: 27 December 2012

Mathematical Reviews number (MathSciNet)
MR1785680

Zentralblatt MATH identifier
1021.35099

#### Citation

Takaoka, Hideo. Well-posedness for the Kadomtsev-Petviashvili II equation. Adv. Differential Equations 5 (2000), no. 10-12, 1421--1443. https://projecteuclid.org/euclid.ade/1356651228.