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Acta Mathematica Vietnamica

Well-posedness of the ADMB–KdV equation in Sobolev spaces of negative indices

icon-email 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.