Summary: This paper addresses well-posedness issues for the initial value problem (IVP) associated with the generalized Zakharov-Kuznetsov equation, namely,
For , the IVP above is shown to be locally well-posed for data in , . For , local well-posedness is shown to hold for data in , , where . Furthermore, for , if and satisfies , then the solution is shown to be global in . For , if , , and satisfies , where is the corresponding ground state solution, then the solution is shown to be global in .