Global well-posedness of the KP-I initial-value problem in the energy space

A. D. Ionescu; C. E. Kenig; D. Tataru

doi:10.1007/s00222-008-0115-0

Global well-posedness of the KP-I initial-value problem in the energy space

A. D. Ionescu
, C. E. Kenig
, D. Tataru

Research output: Contribution to journal › Article › peer-review

111 Scopus citations

Abstract

We prove that the KP-I initial-value problem {∂_tu + ∂_x³u - ∂_x ^-1∂_y²u + ∂_x(u ²/2) = 0 on ℝ_x,y² × ℝ_t; u(0) = φ, is globally well-posed in the energy space E¹(ℝ²) = {φ : ℝ² → ℝ : ∥φ∥_E1(ℝ2) ≈ ∥φ∥_L2 + ∥∂_xφ∥_L2 + ∥∂_x ^-1∂_yφ∥_L2 < ∞}.

Original language	English (US)
Pages (from-to)	265-304
Number of pages	40
Journal	Inventiones Mathematicae
Volume	173
Issue number	2
DOIs	https://doi.org/10.1007/s00222-008-0115-0
State	Published - Aug 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-008-0115-0

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title = "Global well-posedness of the KP-I initial-value problem in the energy space",

abstract = "We prove that the KP-I initial-value problem \{∂tu + ∂x3u - ∂x -1∂y2u + ∂x(u 2/2) = 0 on ℝx,y2 × ℝt; u(0) = φ, is globally well-posed in the energy space E1(ℝ2) = \{φ : ℝ2 → ℝ : ∥φ∥E1(ℝ2) ≈ ∥φ∥L2 + ∥∂xφ∥L2 + ∥∂x -1∂yφ∥L2 < ∞\}.",

author = "Ionescu, \{A. D.\} and Kenig, \{C. E.\} and D. Tataru",

year = "2008",

month = aug,

doi = "10.1007/s00222-008-0115-0",

language = "English (US)",

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journal = "Inventiones Mathematicae",

issn = "0020-9910",

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T1 - Global well-posedness of the KP-I initial-value problem in the energy space

AU - Ionescu, A. D.

AU - Kenig, C. E.

AU - Tataru, D.

PY - 2008/8

Y1 - 2008/8

N2 - We prove that the KP-I initial-value problem {∂tu + ∂x3u - ∂x -1∂y2u + ∂x(u 2/2) = 0 on ℝx,y2 × ℝt; u(0) = φ, is globally well-posed in the energy space E1(ℝ2) = {φ : ℝ2 → ℝ : ∥φ∥E1(ℝ2) ≈ ∥φ∥L2 + ∥∂xφ∥L2 + ∥∂x -1∂yφ∥L2 < ∞}.

AB - We prove that the KP-I initial-value problem {∂tu + ∂x3u - ∂x -1∂y2u + ∂x(u 2/2) = 0 on ℝx,y2 × ℝt; u(0) = φ, is globally well-posed in the energy space E1(ℝ2) = {φ : ℝ2 → ℝ : ∥φ∥E1(ℝ2) ≈ ∥φ∥L2 + ∥∂xφ∥L2 + ∥∂x -1∂yφ∥L2 < ∞}.

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DO - 10.1007/s00222-008-0115-0

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SN - 0020-9910

VL - 173

SP - 265

EP - 304

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 2

ER -

Global well-posedness of the KP-I initial-value problem in the energy space

Abstract

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