RANDOM DATA THEORY FOR THE CUBIC FOURTH-ORDER NONLINEAR SCHRODINGER EQUATION

被引：3

作者：

Van Duong Dinh ^{[1
,2
]}

机构：

[1] Univ Lille, CNRS, UMR 8524, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[2] HCMC Univ Educ, Dept Math, 280 An Duong Vuong, Ho Chi Minh, Vietnam

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 02期

关键词：

Fourth-order nonlinear Schrodinger equation; almost sure well-posedness; wiener randomization; probabilistic Strichartz estimates; GLOBAL WELL-POSEDNESS; DATA CAUCHY-THEORY; WAVE-EQUATIONS; SCATTERING; NLS;

D O I：

10.3934/cpaa.2020284

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the cubic nonlinear fourth-order Schrodinger equation i partial derivative(t)u - Delta(2)u + mu Delta u = +/-vertical bar u vertical bar(2)u, mu >= 0 on R-N, N >= 5 with random initial data. We prove almost sure local well-posedness below the scaling critical regularity. We also prove probabilistic small data global well-posedness and scattering. Finally, we prove the global well-posedness and scattering with a large probability for initial data randomized on dilated cubes.

引用

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页码：651 / 680

页数：30

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