Luiz G. Farah, Hongwei Wang
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  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
| Hongwei Wang |
Faculty of Science, Xi'an Jiaotong University
Xi'an 710049, China
Department of Mathematics, Xinxiang College
Xinxiang 453003, China
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