Ill-posedness results for the (generalized) Benjamin-Ono-Zakharov-Kuznetsov equation.

Here we consider results concerning ill-posedness for the Cauchy problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation, namely, <DIV ALIGN="CENTER" CLASS="mathdisplay"> \begin{displaymath} \left\{ \begin{array}{ll} u_t-\mathscr{H}u_{xx}+u_{xyy}+u^ku... ...b{R}^+, \\ u(x,y,0)=\phi(x,y). \end{array}\right.\tag*{(IVP)} \end{displaymath} For $ k=1$ $ H^{s_1,s_2}(\mathbb{R}^2), s_1,s_2\in \mathbb{R}$ ill-posedness is shown to hold in $ H^{s_1,s_2}(\mathbb{R}^2), 2s_1+s_2<3/2-2/k$, and some particular values of $ s_1,s_2$ [ABSTRACT FROM AUTHOR]