Differential and Integral Equations

Global low-regularity solutions for Kadomtsev-Petviashvili equation

N. Tzvetkov

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Abstract

We study the initial value problem for the KP-II equation. We prove the existence of solutions to the integral equation corresponding to KP-II for any data in $L^2$, removing the additional condition imposed in [15]. Following a method recently developed by J. Bourgain we obtain global solutions to KP-II with data below $L^2$.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1289-1320.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061127

Mathematical Reviews number (MathSciNet)
MR1787069

Zentralblatt MATH identifier
0977.35125

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Tzvetkov, N. Global low-regularity solutions for Kadomtsev-Petviashvili equation. Differential Integral Equations 13 (2000), no. 10-12, 1289--1320. https://projecteuclid.org/euclid.die/1356061127.


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