Local well-posedness for the Sixth-Order Boussinesq Equation

Luiz Gustavo Farah, Amin Esfahani

Published 2010-12-22Version 1

This work studies the local well-posedness of the initial-value problem for the nonlinear sixth-order Boussinesq equation $u_{tt}=u_{xx}+\beta u_{xxxx}+u_{xxxxxx}+(u^2)_{xx}$, where $\beta=\pm1$. We prove local well-posedness with initial data in non-homogeneous Sobolev spaces $H^s(\R)$ for negative indices of $s \in \R$.