Local well-posedness for the Sixth-Order Boussinesq Equation

Abstract

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 $\beta =\pm 1$. We prove local well-posedness with initial data in non-homogeneous Sobolev spaces $H^s(\mathbb{R})$ for negative indices of $s\in \mathbb{R}$.

16 pages. Submitted

References in corpus (1)

• Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation