## Advances in Differential Equations

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1356651228

**Mathematical Reviews number (MathSciNet)**

MR1785680

**Zentralblatt MATH identifier**

1021.35099

**Subjects**

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Secondary: 35A05 35B35: Stability 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]

#### 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