Large time asymptotics for the fourth-order nonlinear Schrodinger equation

被引：16
|
作者：
Hayashi, Nakao [1 ]
Naumkin, Pavel I. [2 ]
机构：
[1] Osaka Univ, Grad Sch Sci, Dept Math, Osaka, Tokyonaka 5600043, Japan
[2] Ctr Ciencias Matemat, Morelia 58089, Michoacan, Mexico
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 258卷 / 03期
关键词：
Fourth-order nonlinear Schrodinger equation; Large time asymptotics; GLOBAL WELL-POSEDNESS; VORTEX FILAMENT; DIMENSIONS; DISPERSION;
D O I：
10.1016/j.jde.2014.10.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Cauchy problem for the fourth-order nonlinear Schrodinger equation in the super critical case i partial derivative(t)u + 1/4 partial derivative(4)(x)u = lambda partial derivative(x)(vertical bar u vertical bar(rho-1)u), where rho > 4, lambda is an element of C. We prove the global existence and the large time asymptotics of solutions for small initial data u(0) is an element of H-1 boolean AND H-1/2,H-1, when the order of the nonliuearity rho >4. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：880 / 905
页数：26
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