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

页码：651 / 680

页数：30

共 50 条

[41] Soliton Solutions and Conservation Laws for an Inhomogeneous Fourth-Order Nonlinear Schrodinger Equation
Wang, Pan
Qi, Feng-Hua
Yang, Jian-Rong
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2018, 58 (11) : 1856 - 1864
[42] Bifurcations and traveling wave solutions for a fourth-order integrable nonlinear Schrodinger equation
Liu, Minghuan
Zheng, Yuanguang
OPTIK, 2022, 255
[43] LOW REGULARITY A PRIORI ESTIMATES FOR THE FOURTH ORDER CUBIC NONLINEAR SCHRODINGER EQUATION
Seong, Kihoon
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (12) : 5437 - 5473
[44] Exact solutions and optical soliton solutions for the nonlinear Schrodinger equation with fourth-order dispersion and cubic-quintic nonlinearity
Zayed, Elsayed M. E.
Al-Nowehy, Abdul-Ghani
RICERCHE DI MATEMATICA, 2017, 66 (02) : 531 - 552
[45] Higher-order localized wave solutions to a coupled fourth-order nonlinear Schrodinger equation
Song, N.
Shang, H. J.
Zhang, Y. F.
Ma, W. X.
MODERN PHYSICS LETTERS B, 2022, 36 (26N27):
[46] The Cauchy problem for the fourth-order Schrodinger equation in Hs
Liu, Xuan
Zhang, Ting
JOURNAL OF MATHEMATICAL PHYSICS, 2021, 62 (07)
[47] The global solution of anisotropic fourth-order Schrodinger equation
Su, Hailing
Guo, Cuihua
ADVANCES IN DIFFERENCE EQUATIONS, 2019,
[48] ON THE MANAGEMENT FOURTH-ORDER SCHRODINGER-HARTREE EQUATION
Banquet, Carlos
Villamizar-Roa, Elder J.
EVOLUTION EQUATIONS AND CONTROL THEORY, 2020, 9 (03): : 865 - 889
[49] THE FOCUSING ENERGY-CRITICAL FOURTH-ORDER SCHRODINGER EQUATION WITH RADIAL DATA
Pausader, Benoit
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (04) : 1275 - 1292
[50] Modulational instability of the higher-order nonlinear Schrodinger equation with fourth-order dispersion and quintic nonlinear terms
Hong, Woo-Pyo
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2006, 61 (5-6): : 225 - 234

← 1 2 3 4 5 →