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

被引：109

作者：

Ionescu, A. D. ^{[1
]}

Kenig, C. E. ^{[2
]}

Tataru, D. ^{[3
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[3] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

INVENTIONES MATHEMATICAE | 2008年 / 173卷 / 02期

基金：

英国科研创新办公室;

关键词：

D O I：

10.1007/s00222-008-0115-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the KP-I initial-value problem {partial derivative(t)u + partial derivative(3)(x)u - partial derivative(-1)(x)partial derivative(2)(y)u + partial derivative(x)(u(2)/2) = 0 on R-x,y(2) x R-t; u(0) =phi is globally well-posed in the energy space E-1(R-2) = {phi : R-2 -> R : parallel to phi parallel to(E1(R2)) approximate to parallel to phi parallel to(L2) + parallel to partial derivative(x)phi parallel to(L2) + parallel to partial derivative(-1)(x)partial derivative(y)phi parallel to(L2) < infinity}.

引用

页码：265 / 304

页数：40

共 31 条

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