Cauchy problem for the Ostrovsky equation

被引：76
|
作者：
Varlamov, V [1 ]
Liu, Y
机构：
[1] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA
[2] Univ Texas, Dept Math, Arlington, TX 76019 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2004年 / 10卷 / 03期
关键词：
Ostrovsky equation; Cauchy problem; construction of solutions; longtime asymptotics;
D O I：
10.3934/dcds.2004.10.731
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Considered herein is an initial-value problem for the Ostrovsky equation that arises in modelling the unidirectional propagation of long waves in a rotating homogeneous incompressible fluid. Nonlinearity and dispersion are taken into account, but dissipation is ignored. Local- and global-in-time solvability is investigated. For the case of positive dispersion a fundamental solution of the Cauchy problem for the linear equation is constructed, and its asymptotics is calculated as t --> infinity, x/t = const. For the nonlinear problem solutions are constructed in the form of a series and the analogous long-time asymptotics is obtained.
引用
收藏
页码：731 / 753
页数：23
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