Well-posedness for the nonlinear fractional Schrodinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation

被引：65
作者：
Guo, Boling [1 ]
Huo, Zhaohui [2 ]
机构：
[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2013年 / 16卷 / 01期
关键词：
fractional Schrodinger equation; fractional Ginzburg-Landau equation; well-posedness; inviscid limit behavior; SPACES; MEDIA;
D O I：
10.2478/s13540-013-0014-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The well-posedness for the Cauchy problem of the nonlinear fractional Schrodinger equation u(t) + i(-Delta)(alpha)u + i vertical bar u vertical bar(2)u = 0, (x, t) is an element of R-n x R, 1/2 < alpha < 1 is considered. The local well-posedness in subcritical space H-s with s > n/2 -alpha is obtained. Moreover, the inviscid limit behavior of solution for the fractional Ginzburg-Landau equation u(t) + (nu+i)(-Delta)(alpha)u + i vertical bar u vertical bar(2)u - 0 is also considered. It is shown that the solution of the fractional Ginzburg-Landau equation converges to the solution of nonlinear fractional Schrodinger equation in the natural space C([0, T]; H-s) with s > n/2 - alpha if nu tends to zero.
引用
收藏
页码：226 / 242
页数：17
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