English

On the Cauchy problem associated to a regularized Benjamin-Ono--Zakharov-Kuznetsov (rBO-ZK) type equation

Analysis of PDEs 2018-11-29 v1

Abstract

In this work we shall study the well-posedness and ill-posedness of the Cauchy problem associated to the equation \begin{equation*} u_{t}+a(u^{n})_{x}+(b\mathscr{H} u_{t}+u_{yy})_{x}=0, \end{equation*} in anisotropic weigthed Sobolev spaces. In particular, we examine the unique continuation property for solutions, of this, with polynomial decay.

Keywords

Cite

@article{arxiv.1811.11447,
  title  = {On the Cauchy problem associated to a regularized Benjamin-Ono--Zakharov-Kuznetsov (rBO-ZK) type equation},
  author = {Fabián Sánchez S. and Félix H. Soriano M.},
  journal= {arXiv preprint arXiv:1811.11447},
  year   = {2018}
}