Local and global Cauchy problems for the Kadomtsev-Petviashvili (KP-II) equation in Sobolev spaces of negative indices

被引：48

作者：

Isaza, P ^{[1
]}

Mejía, J ^{[1
]}

机构：

[1] Univ Nacl Colombia, Dept Math, Medellin, Colombia

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2001年 / 26卷 / 5-6期

关键词：

D O I：

10.1081/PDE-100002387

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is proved that the Cauchy problem for the Kadomtsev-Petviashvili II (KPII) equation is locally well posed in the anisotropic Sobolev spaces H-s1s2 (R-2) with s(1) > -(1)/(3) and s(2) greater than or equal to 0, and globally well posed in H-s10 (R-2) With S-1 > -(1)/(64).

引用

页码：1027 / 1054

页数：28

共 11 条

[1]

Bourgain J, 1998, INT MATH RES NOTICES, V1998, P253

[2]

Bourgain J., 1993, GEOM FUNCT ANAL, V3, P209

[3]

Bourgain J., 1993, GEOM FUNCT ANAL, V3, P209

[4]

Ginibre J, 1996, ASTERISQUE, P163

[5]

ISAZA P, IN PRESS DIFF INT EQ

[6] THE CAUCHY-PROBLEM FOR THE KORTEWEG-DEVRIES EQUATION IN SOBOLEV SPACES OF NEGATIVE INDEXES [J].

KENIG, CE ;

PONCE, G ;

VEGA, L .

DUKE MATHEMATICAL JOURNAL, 1993, 71 (01) :1-21

[7] A bilinear estimate with applications to the KdV equation [J].

Kenig, CE ;

Ponce, G ;

Vega, L .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (02) :573-603

[8]

TAKAOKA H, 1999, LOCAL REGULARITY KAD

[9]

TAKAOKA H, 1998, WELL POSEDNESS KADOM

[10] On the Cauchy problem for Kadomtsev-Petviashvili equation [J].

Tzvetkov, N .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (7-8) :1367-1397

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