14 research outputs found
Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation
We show that the initial value problem associated to the dispersive
generalized Benjamin-Ono-Zakharov-Kuznetsov equationis locally
well-posed in the spaces , s\textgreater{}\frac 2\alpha-\frac 34,
endowed with the normAs a consequence, we get the
global well-posedness in the energy space as soon as
\alpha\textgreater{}\frac 85. The proof is based on the approach of the short
time Bourgain spaces developed by Ionescu, Kenig and Tataru \cite{IKT} combined
with new Strichartz estimates and a modified energy.Comment: arXiv admin note: text overlap with arXiv:1205.0169 by other author