Luiz G. Farah, Hongwei Wang
Abstract:
We show that the Cauchy problem for the defocusing generalized Boussinesq
equation
on the real line is globally well-posed in
with
s>1-(1/(3k)). To do this, we use the I-method, introduced by
Colliander, Keel, Staffilani, Takaoka and Tao [8,9],
to define a modification of the energy functional that is almost
conserved in time. Our result extends a previous result obtained
by Farah and Linares [16] for the case k=1.
Submitted October 3, 2011. Published March 16, 2012.
Math Subject Classifications: 35B30, 35Q55.
Key Words: Boussinesq equation; global well-posedness; I-method.
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Luiz G. Farah ICEx, Universidade Federal de Minas Gerais Av. Ant&ocric;nio Carlos, 6627, Caixa Postal 702, 30123-970 Belo Horizonte-MG, Brazil email: lgfarah@gmail.com | |
Hongwei Wang Faculty of Science, Xi'an Jiaotong University Xi'an 710049, China Department of Mathematics, Xinxiang College Xinxiang 453003, China email: wang.hw@stu.xjtu.edu.cn |
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