Cauchy problem for the Ostrovsky equation in spaces of low regularity

被引：24
|
作者：
Isaza, Pedro [1 ]
Mejia, Jorge [1 ]
机构：
[1] Univ Nacl Colombia, Escuela Matemat, AA-3840 Medellin, Colombia
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2006年 / 230卷 / 02期
关键词：
nonlinear dispersive equations; local solutions;
D O I：
10.1016/j.jde.2006.04.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we consider the initial value problem for the Ostrovsky equation: at partial derivative(t)u - partial derivative(3)(x)u -/+ partial derivative(-1)(x) u + u partial derivative(x)u = 0, x is an element of R, t is an element of R, u (x, 0) = u(0) (x), with initial data in Sobolev spaces H-s(R). Using Bourgain spaces, we prove that the problem is locally well-posed for s > -1/2 if the sign of the third term of the equation is "-" and for s > -3/4 if the sign of this term is "+". (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：661 / 681
页数：21
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