Well-posed initial-boundary value problems for the Zakharov-Kuznetsov equation - Andrei V. Faminskii (Electronic Journal of Differential Equations, 2008)
This paper deals with non-homogeneous initial-boundary value problems for the Zakharov-Kuznetsov equation, which is one of the variants of multidimensional generalizations of the Korteweg-de Vries equation. Results on local and global well-posedness are established in a scale of Sobolev-type spaces under natural assumptions on initial and boundary data.