Well-posedness for the two dimensional generalized Zakharov-Kuznetsov equation in anisotropic weighted Sobolev spaces
Analysis of PDEs
2015-10-14 v2
Abstract
We consider the well-posedness of the initial value problem associated to the k-generalized Zakharov-Kuznetsov equation in fractional weighted Sobolev spaces. Our method of proof is based on the contraction mapping principle and it mainly relies on the well-posedness results recently obtained for this equation in the Sobolev spaces H^s(\R^2) and a new pointwise commutator type formula involving the group induced by the linear part of the equation and the fractional anisotropic weights to be considered
Keywords
Cite
@article{arxiv.1501.00220,
title = {Well-posedness for the two dimensional generalized Zakharov-Kuznetsov equation in anisotropic weighted Sobolev spaces},
author = {German E. Fonseca and Miguel A. Pachon},
journal= {arXiv preprint arXiv:1501.00220},
year = {2015}
}