Global existence of small solutions to the quadratic nonlinear Schrodinger equations in two space dimensions

被引：4

作者：

Hayashi, N

Naumkin, PI

机构：

[1] Tokyo Univ Sci, Dept Appl Math, Tokyo 1628601, Japan

[2] Univ Michoacana, Inst Fis & Matemat, Morelia 58040, Michoacan, Mexico

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2001年 / 32卷 / 06期

关键词：

nonlinear Schrodinger equations; global existence; quadratic nonlinearities; two spatial dimensions;

D O I：

10.1137/S0036141000372532

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a global existence in time of small solutions to the quadratic nonlinear Schrodinger equation in two space dimensions, (0.1) [GRAPHICS] where [GRAPHICS] lambda (j)k, mu (j)k is an element of C. We prove that if the initial data u 0 satisfy some analyticity and smallness conditions in a suitable norm, then the solution of the Cauchy problem (0.1) exists globally in time. Furthermore we prove the existence of the usual scattering states.

引用

页码：1390 / 1403

页数：14

共 50 条

[1] ALMOST GLOBAL EXISTENCE OF SMALL SOLUTIONS TO QUADRATIC NONLINEAR SCHRODINGER-EQUATIONS IN 3 SPACE DIMENSIONS
GINIBRE, J
HAYASHI, N
MATHEMATISCHE ZEITSCHRIFT, 1995, 219 (01) : 119 - 140
[2] GLOBAL EXISTENCE OF SMALL SOLUTIONS TO QUADRATIC NONLINEAR SCHRODINGER-EQUATIONS
HAYASHI, N
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (7-8) : 1109 - 1124
[3] Small data global existence for a class of quadratic derivative nonlinear Schrodinger systems in two space dimensions
Sakoda, Daisuke
Sunagawa, Hideaki
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (04) : 1722 - 1749
[4] GLOBAL EXISTENCE OF SMALL SOLUTIONS FOR A QUADRATIC NONLINEAR FOURTH-ORDER SCHRODINGER EQUATION IN SIX SPACE DIMENSIONS
Aoki, Kazuki
TOHOKU MATHEMATICAL JOURNAL, 2021, 73 (01) : 49 - 98
[5] Global existence of small solutions to nonlinear Schrodinger equations
Hayashi, N
Hirata, H
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 31 (5-6) : 671 - 685
[6] Quadratic derivative nonlinear Schrodinger equations in two space dimensions
Bernal-Vilchis, Fernando
Hayashi, Nakao
Naumkin, Pavel I.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2011, 18 (03): : 329 - 355
[7] NONEXISTENCE OF ASYMPTOTICALLY FREE SOLUTIONS FOR QUADRATIC NONLINEAR SCHRODINGER EQUATIONS IN TWO SPACE DIMENSIONS
Shimomura, Akihiro
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2005, 18 (03) : 325 - 335
[8] Global existence of small analytic solutions to Schrodinger equations with quadratic nonlinearity
Hayashi, N
Kato, K
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1997, 22 (5-6) : 773 - 798
[9] Global existence of small classical solutions to nonlinear Schrodinger equations
Ozawa, Tohru
Zhai, Jian
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (02): : 303 - 311
[10] Global Existence for Two Dimensional Quadratic Derivative Nonlinear Schrodinger Equations
Hayashi, Nakao
Naumkin, Pavel I.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2012, 37 (04) : 732 - 752

← 1 2 3 4 5 →