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.
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页码：651 / 680
页数：30
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