Bilinear estimates and applications to 2D NLS

被引：65

作者：

Colliander, JE ^{[1
]}

Delort, JM

Kenig, CE

Staffilani, G

机构：

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

[2] Univ Paris 13, Dept Math, F-93430 Villetaneuse, France

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

[4] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 353卷 / 08期

关键词：

nonlinear Schrodinger equation; nonlinear dispersive equations; weak turbulence; NLS blow-up; bilinear estimates; multilinear harmonic analysis; Strichartz inequalities;

D O I：

10.1090/S0002-9947-01-02760-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The three bilinearities uv, (uv) over bar (u) over barv for functions u, v : R-2 x [0, T] bar right arrow C are sharply estimated in function spaces X-s,X-b associated to the Schrodinger operator i partial derivative (t) + Delta. These bilinear estimates imply local wellposedness results for Schrodinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cubic nonlinear Schrodinger equation (and certain generalizations) are also obtained.

引用

页码：3307 / 3325

页数：19

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