Scattering for the Zakharov System in 3 Dimensions

被引：0
作者：
Zaher Hani
Fabio Pusateri
Jalal Shatah
机构：
[1] New York University,Courant Institute of Mathematical Sciences
[2] Princeton University,Department of Mathematics
来源：
Communications in Mathematical Physics | 2013年 / 322卷
关键词：
Cauchy Problem; Decay Estimate; Wave Operator; Wave Component; Langmuir Wave;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t−1, whereas the Schrödinger component decays almost at a rate of t−7/6.
引用
收藏
页码：731 / 753
页数：22
相关论文
共 50 条
[41]   GLOBAL REGULAR SOLUTIONS FOR THE 3D ZAKHAROV-KUZNETSOV EQUATION POSED ON A BOUNDED DOMAIN [J].
Larkin, N. A. .
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2016, 29 (7-8) :775-790
[42]   On exponential decay properties of solutions of the (3+1)-dimensional modified Zakharov-Kuznetsov equation [J].
Chong, Gezi ;
He, Jianxia .
ELECTRONIC RESEARCH ARCHIVE, 2025, 33 (01) :447-470
[43]   Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation [J].
Klein, Christian ;
Roudenko, Svetlana ;
Stoilov, Nikola .
PHYSICA D-NONLINEAR PHENOMENA, 2021, 423 (423)
[44]   GLOBAL EXISTENCE AND SCATTERING FOR SOLUTIONS OF FINITE MASS OF THE CUBIC SCHROEDINGER EQUATION IN TWO DIMENSIONS [J].
Planchon, Fabrice .
ASTERISQUE, 2012, (348) :425-447
[45]   GLOBAL WELL-POSEDNESS FOR THE 3D ZAKHAROV-KUZNETSOV EQUATION IN ENERGY SPACE H [J].
Huo, Zhaohi ;
Jia, Yueling ;
Li, Qiaoxin .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2016, 9 (06) :1797-1851
[46]   Modified scattering for the higher-order anisotropic nonlinear Schrodinger equation in two space dimensions [J].
Hayashi, Nakao ;
Naumkin, Pavel, I .
JOURNAL OF MATHEMATICAL PHYSICS, 2021, 62 (07)
[47]   Schrodinger-improved Boussinesq system in two space dimensions [J].
Ozawa, Tohru ;
Tomioka, Kenta .
JOURNAL OF EVOLUTION EQUATIONS, 2022, 22 (02)
[48]   DISPERSIVE LIMIT OF THE EULER-POISSON SYSTEM IN HIGHER DIMENSIONS [J].
Pu, Xueke .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (02) :834-878
[49]   LOCAL AND GLOBAL WELL-POSEDNESS IN THE ENERGY SPACE FOR THE DISSIPATIVE ZAKHAROV-KUZNETSOV EQUATION IN 3D [J].
Darwich, Mohamad .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (09) :3715-3724
[50]   Global Regular Solutions to One Problem of Saut-Temam for the 3D Zakharov-Kuznetsov Equation [J].
Larkin, N. A. ;
Padilha, M. V. .
APPLIED MATHEMATICS AND OPTIMIZATION, 2018, 77 (02) :253-274
12345