Search

Considered herein is the dissipation-modified Kadomtsev–Petviashvili equation in two space-dimensional case. It is established that the Cauchy problem associated to this equation is locally well-posed in anisotropic Sobolev spaces. It is also shown in some sense that this result is sharp. In addition, the global well-posedness for this equation under suitable conditions is proved.

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 $s \in \R$., Comment: 16 pages. Submitted