%0 Journal Article
%T On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations
%A Axel Gruenrock
%J Electronic Journal of Differential Equations
%D 2009
%I Texas State University
%X The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation $$ u_t + u_{xxx} + partial_x^{-1}u_{yy}= (u^l)_x, quad l ge 3, $$ is shown to be locally well-posed in almost critical anisotropic Sobolev spaces. The proof combines local smoothing and maximal function estimates as well as bilinear refinements of Strichartz type inequalities via multilinear interpolation in $X_{s,b}$-spaces.
%K Cauchy-problem
%K local well-posedness
%K generalized KP-II equations
%U http://ejde.math.txstate.edu/Volumes/2009/82/abstr.html