Well-posedness of the ADMB–KdV equation in Sobolev spaces of negative indices
Amin Esfahani
,
Reza Pourgholi
Abstract
In this paper, we study the ADMB–KdV equation. We show that the associated initial value problem is locally well posed in Sobolev spaces $H^s(\mathbb R^2)$ for $s > −1/2$. We also prove that our result is sharp in some sense.