Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 82, pp. 1-9.

Title: On the Cauchy-problem for generalized
       Kadomtsev-Petviashvili-II equations

Author: Axel Grunrock (Rheinische Friedrich-Wilhelms-Univ., Germany)

Abstract:
 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.
 
Submitted April 9, 2009. Published July 10, 2009. 
Math Subject Classifications: 35Q53.
Key Words: Cauchy-problem; local well-posedness; 
           generalized KP-II equations.