%0 Journal Article
%T Global solutions in lower order Sobolev spaces for the generalized Boussinesq equation
%A Luiz G. Farah
%A Hongwei Wang
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X We show that the Cauchy problem for the defocusing generalized Boussinesq equation $$ u_{tt}-u_{xx}+u_{xxxx}-(|u|^{2k}u)_{xx}=0, quad kgeq 1, $$ on the real line is globally well-posed in $H^s(mathbb{R})$ 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.
%K Boussinesq equation
%K global well-posedness
%K I-method
%U http://ejde.math.txstate.edu/Volumes/2012/41/abstr.html