Global solutions for the generalized Boussinesq equation in low-order Sobolev spaces

Luiz Gustavo Farah, Hongwei Wang

We show that the Cauchy problem for the defocusing generalized Boussinesq equation $u_{tt}-u_{xx}+u_{xxxx}-(|u{|}^{2k}u{)}_{xx}=0$, $k\ge 1$, on the real line is globally well-posed in…