| Title: |
A note on the Cauchy problem for the 2D generalized Zakharov-Kuznetsov equations |
| Authors: |
Vento, Stéphane, Ribaud, Francis |
| Publication Year: |
2011 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Analysis of PDEs |
| More Details: |
In this note we study the generalized 2D Zakharov-Kuznetsov equations $\partial_tu+\Delta\partial_xu+u^k\partial_xu=0$ for $k\ge 2$. By an iterative method we prove the local well-posedness of these equations in the Sobolev spaces $H^s(\mathbb{R}^2)$ for $s>1/4$ if $k=2$, $s>5/12$ if $k=3$ and $s>1-2/k$ if $k\ge 4$. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/1111.4384 |
| Accession Number: |
edsarx.1111.4384 |
| Database: |
arXiv |
