A NEKHOROSHEV-TYPE THEOREM FOR THE NONLINEAR SCHRODINGER EQUATION ON THE TORUS

被引:54
作者
Faou, Erwan [1 ,2 ]
Grebert, Benoit [3 ]
机构
[1] INRIA, F-35170 Bruz, France
[2] ENS Cachan Bretagne, F-35170 Bruz, France
[3] Univ Nantes, Lab Math Jean Leray, F-44322 Nantes 3, France
关键词
Nekhoroshev theorem; nonlinear Schrodinger equation; normal forms; BIRKHOFF NORMAL-FORM; HAMILTONIAN-SYSTEMS; STABILITY; PDES;
D O I
10.2140/apde.2013.6.1243
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove a Nekhoroshev type theorem for the nonlinear Schrodinger equation iu(t) = -Delta u + V star u + partial derivative((u) over barg)(u,(u) over bar), x is an element of T-d, where V is a typical smooth Fourier multiplier and g is analytic in both variables. More precisely, we prove that if the initial datum is analytic in a strip of width rho > 0 whose norm on this strip is equal to epsilon, then if epsilon is small enough, the solution of the nonlinear Schrodinger equation above remains analytic in a strip of width rho/2, with norm bounded on this strip by C epsilon over a very long time interval of order epsilon(-sigma)|ln epsilon|(beta), where 0 < beta < 1 is arbitrary and C > 0 and sigma > 0 are positive constants depending on beta and rho.
引用
收藏
页码:1243 / 1262
页数:20
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