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

2009/04/09 by Gruenrock, Axel
#35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.1514

Abstract

The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation u_t + u_xxx + ∂_x^-1u_yy= (u^l)_x, l ≥ 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.

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