Well-Posedness for the Two-dimensional Zakharov-Kuznetsov Equation

Shan Minjie

Well-Posedness for the Two-dimensional Zakharov-Kuznetsov Equation

Analysis of PDEs 2018-08-16 v2

Authors: Shan Minjie

Abstract

We show the global well-posedness for the two-dimensional Zakharov-Kuznetsov equation in $H^{s}({\mathbb{R}^2})$ when $\frac{11}{13}<s<1$ via the I-method. Additionally, local well-posedness for the symmetrized ZK equation in $B^\frac{1}{2}_{2,1}(\mathbb{R}^2)$ is established by using atomic spaces.

Keywords

well-posedness global well-posedness and scattering for nonlinear dispersive equations knizhnik-zamolodchikov equation

Cite

@article{arxiv.1807.10123,
  title  = {Well-Posedness for the Two-dimensional Zakharov-Kuznetsov Equation},
  author = {Shan Minjie},
  journal= {arXiv preprint arXiv:1807.10123},
  year   = {2018}
}

Comments

27 pages

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